Also, Jesus is the Son of David. In the Davidic Kingdom, the Queen Mother sits enthroned at the right hand of the King.
ref: 1 Kings 2:19
bingo !!!! if you hadnt posted this , i was going to.....
Exegetical hallucination.
Solomon spared Adonijah (Solomons older brother) life on the promise of "good behavior" though he did not want to recognize Solomon as the Lords choice for the throne. He then asks Bathsheba to petition the king for Adonijah to take one of David's concubines as his wife. Apparently he thought he could lay claim to the throne by backdooring his way in. Solomon instantly recognizes the plan.
So in reading the context of the passage you cited in 1 Kings 2:19 ... it is absolutely clear (Read the whole chapter) that before Bathsheba approached Solomon on behalf of Adonijah that Bethsheba was NOT, as you say, enthroned at the right hand of the King.
Lets look at the actual text shall we?
1 Kings 2:19
So Bathsheba went to King Solomon to speak to him for Adonijah. And the king arose to meet her, bowed before her, and sat on his throne; then he had a throne set for the king's mother, and she sat on his right.
Solomon saw her coming, acknowledged her, then he sat down, then had a throne brought in for her, obviously one that did not exist before she approached the king. They had their conversation about Adonijah and I will let you read the next couple of verses ... because it mauls your theory. Solomon rejects his mothers request and has Adonijah killed.
After this, Bathsheba is not mentioned in scripture at all ... nothing about her ruling with Solomon, nothing about any successors doing likewise, nothing about David's mother sitting at his right hand, nothing about her or any other woman sitting at the right hand of the Father or the Lord Jesus Christ.
I hope this helps.