There was a prophet named Nathan who came to David and told him the story of a man who had many, many sheep.  "Large flocks." But when a traveler came to his house, the man took the one and only lamb--who was almost a pet--from a very poor man and slaughtered it to feed to his guest.

It made David furious.  He pronounced judgment on the man who killed the lamb.  "He will be put to death."  And Nathan said to David, "You are the man."  David immediately knew that Nathan was talking about him concerning Bathsheba and Uriah.  David thought the entire incident was gone and forgotten, but God knew.  And God sent his prophet to bring David's sin to light.  He was guilty. And the punishment that God gave to him was that the baby would die.

David prayed and prayed.  He confessed.  He begged for the baby boy's life.  But God does what he says he will do.  What David did in secret was uncovered.  And the penalty for sin was death.  If you have never read Psalms 51, read it.  It is a pouring out of David's heart.  His weeping, when he realized that his sin was really against God, and God's authority in David's life.  King or no king.

Bathsheba's heart was broken.  She lost Uriah, she lost her son.  But David was moved to comfort her, "And David comforted Bathsheba..."  Imagine what she was going through.  Her life was shattered.  But soon, they had another son--Solomon.  The Bible says, "...and the Lord loved him."

When David was old, and dying, Adonijah--David's son by Haggith--said, "Now I will be king," (even though he was born after Absalom.)  He got the priest to help him in his effort.  Adonijah called all his brothers except Solomon to a confab.  But Nathan went to Bathsheba, and told her to go to David on his death bed and implore him to make Solomon king.  She did.  She knelt and implored David to name Solomon to reign.  She told him what Adonijah was doing.  Nathan concurred.

So David appointed Solomon as his heir, "...for he shall be king in my stead...I have appointed him to be ruler over Israel and over Judah."  Solomon was anointed king, even though  Bathsheba was the eighth or ninth wife of David.  Solomon was not David's firstborn.  But he was now king.  David loved Bathsheba, and she was favored by David over his other wives.  There must have been a lot of conflict.  But Solomon was an excellent choice for king.  The wisest man in the Old Testament.