For a person to worship some entity or phenomenon or being involves, of necessity, that person regarding that entity or phenomenon or being as being higher or more important than themself.

Being that that is so, does that part of the Triune Godhead called "The Holy Spirit" worship Jesus Christ, the Son of God?
Does that part of the Triune Godhead called "The Father" worship Jesus Christ, the Son of God?

We are merely talking about love - even agape love here. We're instead talking: worship.

Admittedly, there is no one better for any person of the Trinity to not simply admire and even adore or worship (being that all three are perfect - in the fullest and most complete sense of the word), but . . .

Give yourself a hug?

Sounds selfish, or at least non-productive.

IS the long-deceased, redeemed-by-God-her-Savior (see Luke 1:47), former-virgin-when-birthing-Jesus Mary - who is not part of the Triune Godhead - to be worshipped by the Father and/or the Son and/or The Holy Spirit, and is Mary legitimately called "The Mother of God the Father - being that the Son of God is One with and Co-Equal with the Father and the Spirit?

As co-Redemptrix and even Divine Mediator, Mary would leave much to be desired. And speaking to the dead is forbidden according to Holy Writ:

Deuteronomy 18:10 There shall not be found among you any one who burns his son or his daughter as an offering any one who practices divination, a soothsayer, or an augur, or a sorcerer,
11 or a charmer, or a medium, or a wizard, or a necromancer.
12 For whoever does these things is an abomination to the Lord; and because of these abominable practices the Lord your God is driving them out before you.
13 You shall be blameless before the Lord your God.
14 For these nations, which you are about to dispossess, give heed to soothsayers and to diviners; but as for you, the Lord your God has not allowed you so to do.

The saints in glory do pray for whatever to The One On The Throne who fascinates them and who are absorbed in worshipping Him, and we yet-alive ones here in this life do "pray for one another" for (yet not necessarily on behalf) of one another to God, but we mortal humans petitioning dead saints is not simply silly, but even blasphemous, being that God alone (in various persons of the Trinity) is our only Divine Mediator:

Romans 8:26 Likewise the Spirit helps us in our weakness; for we do not know how to pray as we ought, but the Spirit Himself intercedes for us with sighs too deep for words.
Romans 8:27 And He [ not "she"> ] who searches the hearts of humans knows what is the mind of the Spirit, because the Spirit intercedes for the saints according to the will of God.
Romans 8:34 Who is to condemn? Is it Christ Jesus, who died, yes, who was raised from the dead, who is at the right hand of God, who indeed intercedes for us?

First Timothy 2:5 For there is one God, and there is one mediator between God and men, the man Christ Jesus...

While I'm at it, I have some grievances against both the catholic and anglican churches.

The first is concerning catholics who call Mary the mother of Jesus: "Mary, Queen of the clergy, " and the second concerns anglicans who call Christ's ecclesia: "Holy Mother Church."

NO where in the entirety of the Sacred-66-books Holy Bible are those two terms ever used, and what they, in essence, demonically and blasphemously do is elevate feminists and feminism to a level of hierachy and prominence which such aberrations certainly do NOT deserve.

It is true that, as Mary herself stated: "all generations will call me blessed" (Luke 1:48)...but that "blessedness" does NOT require nor mandate inferior-gender Mary to be put on par with the husband-of-one-wife (i.e. one male with one female) male bishops and male deacons who First Timothy 3:2 and First Timothy 3:12 commissions to shepherd those need-to-be-silent-and-subject-to-males inferior gender -- and NOT vice-versa:

First Timothy 2:11 Let a woman learn in silence with all subjection.
12 I allow NO woman to teach or to have authority over men; she is to keep silent.
13 For Adam was formed first, then Eve;
14 and Adam was not deceived, but the woman was deceived and became a transgressor.

MUCH irritation and consternation and confusion can be avoided and alleviated not merely within "the church" but even in secular and civil government and society if the anti-feminist admonition of First Timothy 2:11-14 is taken literally and taken seriously.

"Queen" of the [male] clergy obviously insinuates not simply authoritative guidance in opposition to the clear implication of Song 2:14 ("let me see YOUR face and hear YOUR voice only) but even royal jurisdiction has been presumed to be granted to an admittedly-sexually-pure but needing-redemption-and-now-deceased mere "handmaid of the Lord" who simply was chosen and then willfully involved with a unique-to-be-sure but beyond-her-own-sinful-capacity duty as one of many chosen chaste Jewish young women.

Such should be obvious to all per the following rebuke from Jesus Himself:

Luke 11:27 As He said this, a woman in the crowd raised her voice and said to Him, "Blessed is the womb that bore you, and the breasts that you sucked!"
Luke 11:28 But He said, "Blessed rather are those who hear the word of God and keep it!"

plus:

Mark 3:32 And a crowd was sitting about Him; and they said to Him, "Your mother and your brothers are outside, asking for you."
33 And He replied, "Who are my mother and my brothers?"
34 And looking around on those who sat about Him, He said: "Here are my mother and my brothers!
35 Whoever does the will of God is my brother, and sister, and mother."

and:

Luke 8:20 And He was told, "Your mother and your brothers are standing outside, desiring to see you."
Luke 8:21 But He said to them, "My mother and my brothers are those who hear the word of God and do it."

"Not to mention:"

Luke 14:26 "If any one comes to me and does not HATE his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be my disciple.

So much for the "family is everything" wayward quirkiness uttered by Vin Diesel in the movie Fast Five.

Plain it is that the "Holy Mary, Mother of God" rote mantra....blasphemously blattered by cultic-catholic mindless who are superstitiously dull of mind and/or fearful slaves to self-appointed ecclesiastical pompous flagrantly decorated in fancy flaunted robes and their others-appointed, big-shot, white-collared, religious patsies...is a hard habit to break. But it behooves the sane and sensible to always remember that mere-created-human Mary did not generate nor originate either God the Father Almighty nor did she create nor originate The Holy Spirit.

There are approved ways for mothers to take care of their mis-called "adorable" little brats than making more out of the Mary-with-Jesus and Jesus-with-Mary motherhood thing than should be made, and those ways are found here and there throughout the entirety of Holy Scripture, such as:

Titus 2:3 Bid the older women likewise to be reverent in behavior, not to be slanderers or slaves to drink; they are to teach what is good,
Titus 2:4 and so train the young women to love their husbands and children,
Titus 2:5 to be sensible, chaste, domestic, kind, and submissive to their husbands, that the word of God may not be discredited.

Moreover, although the Latin-based word "catholic" infers "universal" [whatever] to some propaganda peddlers, catholic means the Catholic religion to normal people, like the Latin word peccatore to such persons might be thought of as referring to woodpeckers or henpecking instead the weird and strange equivalent of the word and concept with "sin."

It is evident that not only those of asian religious cults have problems with espousing ancestor worship, but so do catholic deviants who give "dear" relatives (deceased and non-deceased) the same or perhaps even greater importance as their Creator, and thus are sinfully guilty of committing (and not "performing") the following:

Romans 1:25 ...they exchanged the truth about God for a lie and worshiped and served the creature rather than the Creator, who is blessed for ever! Amen.

Concerning the absurd and ridiculous foreign-and-weird-sounding phrase: "Holy Mother Church..."

NO where throughout the entire Scriptures is the assembly of believers (i.e. the ecclesia) ever referred to as a "mother."

A bride - yes; a "mother" - no!

There are named references to "mother" throughout the Bible:

Genesis 17:16 "I will bless [Sarah], and moreover I will give you a son by her; I will bless her, and she shall be a mother of nations; kings of peoples shall come from her."

Genesis 37:10 But when [Joseph] told [his dream] to his father and to his brothers, his father rebuked him, and said to him, "What is this dream that you have dreamed? Shall I and your mother and your brothers indeed come to bow ourselves to the ground before you?"

Get this:

Deuteronomy 27:23 "Cursed be he who lies with his mother-in-law." And all the people shall say, 'Amen.'

No problem. Be sure to tell my jealous wife that one.

Judges 5:7 The peasantry ceased in Israel, they ceased until you arose, Deborah, arose as a mother in Israel.

So far, both Sarah and Debbie comprised "the Mothers of Israel."

First Samuel 20:30 Then Saul's anger was kindled against Jonathan, and he said to him, "You son of a perverse, rebellious woman, do I not know that you have chosen the son of Jesse to your own shame, and to the shame of your mother's nakedness?"

Thought that I'd throw that one in there, just for kicks, to prepare you for the b---- word.

Here's one for the abortionists:

Job 3:1 After this Job opened his mouth and cursed the day of his birth.
2 And Job said:
3 "Let the day perish wherein I was born, and the night which said, 'A man-child is conceived.'
4 Let that day be darkness! May God above not seek it, nor light shine upon it.
5 Let gloom and deep darkness claim it. Let clouds reside upon it; let the blackness of the day terrify it.
6 That night: let thick darkness seize it! let it not rejoice among the days of the year, let it not come into the number of the months.
7 Yes, let that night be barren; let no joyful cry be heard in it.
8 Let those curse it who curse the day, who are skilled to rouse up Leviathan.
9 Let the stars of its dawn be dark; let it hope for light, but have none, nor see the eyelids of the morning;
10 because it did not shut the doors of my mother's womb, nor hide trouble from my eyes.
11 Why did I not die at birth, come forth from the womb and expire?"

Ditto with:

Jeremiah 20:14 Cursed be the day on which I was born! The day when my mother bore me, let it not be blessed!
Jeremiah 20:17 because he did not kill me in the womb; so my mother would have been my grave, and her womb forever great. [ albeit bloated and infected ]

The point is to NOT terminate the development of prophets of the Lord in the wombs of their mothers, being that the terminators will themselves be then terminated, sooner or later, temporally and eternally in everlasting punishment.

Back to Mary.

Luke 1:43 And why is this granted me, that the mother of my Lord [ the word is NOT in all-capital letters signifying Trinity, and is an inferior-gender blurb uttered by inferior-gender Elizabeth in which she is hopefully not giving Mary the credit for generating and thus being self-conceiving Mother of the Son of God but rather being a who-knows-how-that-happened womb-caretaker mother of the Son of Man ] should come to me?

That is about as close as one can perilously come to the blasphemous phrase: "Mary, Mother of GOD [the Father and God the Holy Spirit]."

John 2:3 When the wine failed, the mother of Jesus said to him, "They have no wine."
John 2:4(?) And Jesus replied: "What OF it? So WHAT, bitch? What am I supposed to do about it? You think I'm some kind of a wimpy mopheaded momma's-boy tit-baby still needing my diapers changed or asking mommy's permission to go to the restroom?"
John 2:5 His mother said to the servants, "Do whatever he tells you."

Did mother Mary have to give Jesus a clue or an idea what He should do at that time? And how He should do it?

What did Mary have in mind: not simply Jesus making wine (but neither cigarettes nor heroin nor playboy for mass dissemination), but also getting news publicity as a Wonder Worker with consequential money then pouring into the Joseph-and-Mary-Foundation coffers, and even eventually overthrowing the idolatrous Roman-gods-worshipping Roman government?

John 2:4 And Jesus said to her, "Oh woman [ why not: "Oh mommy?" ], what have you to do with me? My hour has not yet come."

John 19:26 When Jesus saw His mother, and the disciple whom He loved [ back off on that one, all you homoqueer insinuators and misinterpreters! ] standing near, He said to His mother, "Woman [ why not: "Mommy?" ], hey, your son!"
John 19:27 Then He said to the disciple, "Hey, your mother!" And from that hour the disciple took her to his own home. [ and did what to and with her thereafter? ]

Not quite his biological mother, Jesus, but I don't think you meant to imply disoriented hallucination under crucifixional duress, but only caretakership - not as some extrapolated command to make Mary the "Mother Church."

Acts 1:14 All these with one accord devoted themselves to prayer, together with the women and Mary the mother of Jesus [ why not "Mother of GOD?" ], and with his brothers.

Romans 16:13 Greet Rufus, eminent in the Lord, also his mother and mine. [ biologically, Paul? ] Another pseudo-proof for "Holy Mother Church?"

Galatians 4:26 But the Jerusalem above is free, and she is our mother. [ I assume that the matriarchal term is symbolical or metaphorical? Or another pseudo-proof for "Mother Church?" ]

Revelation 17:5 ...and on her forehead was written a name of mystery: "Babylon the great, mother of harlots [ a contrast to "Holy Mother Church" ] and of earth's abominations."

No, the ecclesia of Christ is NOT called "Holy Mother Church," but rather:

Revelation 19:7 Let us rejoice and exult and give him the glory, for the marriage of the Lamb has come, and His Bride has made herself ready;
Revelation 21:2 And I saw the holy city, new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband;
Revelation 21:9 Then came one of the seven angels who had the seven bowls full of the seven last plagues, and spoke to me, saying, "Come, I will show you the Bride, the Wife of the Lamb."
Revelation 22:17 The Spirit and the Bride say, "Come." And let him who hears say, "Come." And let him who is thirsty come, let him who desires take the water of life without price.