There is no reference in scripture to a position of "Queen" in the new Heaven, or the new Earth. There is no indication in Scripture that God desires, wants, or will have a "Queen", or that this "Queen" will serve with Jesus, the King of Kings.
Psalm 45:9 doesn't refer to God, it refers to David's earthly King, who did have a Queen:
Thou lovest righteousness, and hatest wickedness: therefore God, thy God, hath anointed thee with the oil of gladness above thy fellows.Note that God is referenced in verse 7, and is the God of the "thy" being referenced ("thy God"). So Verse 9's "thy" is the "thy" for whom God is God, not God. Putting them together, "God is your God, and on your right hand the queen stood".8All thy garments smell of myrrh, and aloes, and cassia, out of the ivory palaces, whereby they have made thee glad.
9Kings' daughters were among thy honourable women: upon thy right hand did stand the queen in gold of Ophir.
1st Kings 2:18-19 are not about "intercession", they are about a son wanting to ask his father to get a wife for him, and doing so through the King's mother.
Worse, the result of that "intercession" was that the King refused, mocked his mother for allowing herself to be used, and swore to kill the son for petitioning him through his mother.
Hardly an "example" of some exalted Queen sitting on the right hand of God from whom we should ask for intercession:
18And Bathsheba said, Well; I will speak for thee unto the king.Scripture is not impossible to understand.19Bathsheba therefore went unto king Solomon, to speak unto him for Adonijah. And the king rose up to meet her, and bowed himself unto her, and sat down on his throne, and caused a seat to be set for the king's mother; and she sat on his right hand.
20Then she said, I desire one small petition of thee; I pray thee, say me not nay. And the king said unto her, Ask on, my mother: for I will not say thee nay.
21And she said, Let Abishag the Shunammite be given to Adonijah thy brother to wife.
22And king Solomon answered and said unto his mother, And why dost thou ask Abishag the Shunammite for Adonijah? ask for him the kingdom also; for he is mine elder brother; even for him, and for Abiathar the priest, and for Joab the son of Zeruiah.
23Then king Solomon sware by the LORD, saying, God do so to me, and more also, if Adonijah have not spoken this word against his own life.
I certainly agree with that. I don't agree with your interpretation, though. Do you claim that your interpretation is infallibly correct?
I Kings 2:
13And Adonias the son of Haggith came to Bethsabee the mother of Solomon. And she said to him: Is thy coming peaceable? he answered: Peaceable. 14And he added: I have a word to speak with thee. She said to him: Speak. And he said: 15Thou knowest that the kingdom was nine, and all Israel had preferred me to be their king: but the kingdom is transferred, and is become my brother's: for it was appointed him by the Lord. 16Now therefore I ask one petition of thee: turn not away my face. And she said to him: Say on. 17And he said: I pray thee speak to king Solomon (for he cannot deny thee any thing) to give me Abisag the Sunamitess to wife. 18And Bethsabee said: Well, I will speak for thee to the king. 19Then Bethsabee came to king Solomon, to speak to him for Adonias: and the king arose to meet her, and bowed to her, and sat down upon his throne: and a throne was set for the king's mother, and she sat on his right hand. 20And she said to him: I desire one small petition of thee, do not put me to confusion. And the king said to her: My mother, ask: for I must not turn away thy face.
Obviously, Solomon ended up rejecting her request ... not because she didn't have the right to make it, but because it was an evil request.
The whole of Ps 45 is traditionally interpreted as a Messianic prophecy. Its immediate reference is to Solomon, who was a "type" (foreshadowing) of the Christ (cf 1 Chron 17:12-14). Don't take my word for that, take the word of the author of Hebrews 1:8-9, which quotes Ps 45 verbatim and says it speaks "of the Son".
The "Queen" referenced here is the Queen Mother (of Solomon, that is), who bore the title gebirah ("great lady") in Hebrew. That makes her precisely the "type" (foreshadowing) of the Queen Mother of the true Solomon, Jesus Christ.
Do a word search sometime through the historical books of the OT of how many times it mentions the king's mother (either by name or by relationship). You'll see that they're mentioned often.