Hi Annie,
Here is an excerpt from a Scott Hahn article titles Mary, Holy Mother which elaborates a little more about that verse.
Let’s take a look at an example of the function and authority of the Queen Mother in 1st Kings. In chapter 1 there is an intense fraternal rivalry between Solomon or Jedidiah, whose throne name is Peace, Solomon, and his half-brother, Adonijah, who by the way is older and was born to one of David’s wives whom he had married before Bathsheba. So Adonijah seemed to have a kind of prima facia claim to the throne before Solomon, except that Bathsheba had exacted from David an oath to the effect that her son would get the throne. You can get it in Psalm 110 especially. So, anyway, Adonijah approaches Bathsheba in order to approach Solomon. We’re going to see how this goes. But first of all we see King David asking Bathsheba, verse 17, " What is it you want the king asked? She said to him, ‘My Lord, you yourself swore to me your servant by the Lord your God, Solomon your son shall be king after me and he will sit on my throne. But now Adonijah has become king and you my Lord, the king, do not know about it.’" And it goes on talking about this palace coup attempt.
Then King David says over in verse 28 and 29 calling Bathsheba. “So she came into the king’s presence and stood before him. The king then took an oath, ‘as surely as the Lord lives,’” and he goes on promising and swearing that “Solomon, your son, shall be king after me and he will sit on my throne in my place,” even though the majority of the people were going after Adonijah at the time, several key priests, as well. And so she rejoices.
Now turn over to 1st Kings 2. There’s where David gives his royal charge to Solomon and Solomon asks for wisdom, but just browse and just go through that as quickly as you can and just see what is going on here because it is very unusual. Let’s take a look in particular at verse 13. “Now Adonijah, the son of Haggith, went to Bathsheba, Solomon’s mother. Bathsheba asked him, ‘Do you come peacefully?’ He answered, ‘Yes, peacefully,’ then he added, ‘I have something to say to you.’ ‘You may say it, she replied.’ ‘As you know,’ he said, ‘the kingdom was mine. All Israel looked to me as their king. But then things changed and the kingdom has gone to my brother for it has come to him from the Lord. Now I have just one request to make of you. Do not refuse me.’ 'You may make it she said. So he continued, ‘Please ask King Solomon, he won’t refuse you, to give me Abishag, the Shunamite as my wife.’” If you understood palace politics, you’d see what this was. “Very well,” Bathsheba replied. “I will speak to the king for you.”
Abishag happened to be David’s last lover and wife. She was the one young woman who kept him warm in his old age, sleeping next to him at all times. To have David’s last wife would be to have official claim to the throne. This is why Absolom publicly slept with David’s concubines after he threw his father out of Jerusalem, because if I have the Queen Mothers, if I have the king’s wives, who do you see as your king? Solomon is no fool. When Bathsheba went to King Solomon to speak to him for Adonijah, look what happens. The king of Israel, the son of David, the supreme head of God’s covenant people in the whole world, according to Psalm 2 stood up to meet her, bowed down to her and sat down on his throne and he had a throne brought for the king’s mother and she sat down at his right hand. “Sit at my right hand,” Psalm 110. That’s the position of authority. I have one small request to make of you. She goes on and makes the request. Solomon sees through it. Says no, of course, and executes Adonijah.
But look at the beginning of the institution of the gebirah. It’s something that continues. When the Queen Mother walks in, the king, because he is her son, pays filial homage to her and establishes her at his right hand, upon a throne as Queen Mother. If I am the father of the family of this kingdom, if I am the shepherd of this flock, that makes you the mother. Not only my mother but the grandmother of us all. That institution persisted down through the ages of the Judaite monarchy. There is no evidence of it ever being suppressed by the prophets or criticized by Yahweh or ever falling into hard times and being replaced because it was seen as something that was meaningless.