1 Kings 2:19-20

1 Kings 2:19-20 King James Version (KJV)
19 Bathsheba 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.
20 Then 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.

Easy English Bible
So Bathsheba went to King Solomon, to speak on behalf of Adonijah. The king stood up to meet her. He was polite to her. Then he sat down on his *throne. And he *ordered (his servants to bring) another *throne for his mother. So she sat down at his right side. v20 ‘I have one small thing to ask you’, she said. ‘Do not refuse me.’ And the king answered her, ‘Ask me, mother! I will not refuse you!
© 1997-2008, Wycliffe Associates (UK)

These are my thoughts, please share yours.
19 Bathsheba actually did as she was asked even though he made much trouble for her and Solomon her son. Solomon shows respect to his mother even though he is king the scripture says to honor your father and mother does not give exceptions for kings. The right was often times the place where the queen set or where a head advisor set, Jesus sets at the right of the Father. Solomon at this time may have not had a queen so Bathsheba being his mother may have been the highest honored woman in the country at the time.
20 She comes to him in a similar way as Adonijah came to her. Solomon may have thought the request was on her behalf which he have done nearly anything for her, to show her honor, she was now a widow and Solomon was the one to care for her until she died or remarried by Jewish law.