For the time being I am ignoring the fact that David had many wives. This will certainly come up later on. The civil war continued between David (Judah) and the house of Saul (Israel), but over time it became more obvious that David was going to win. Abner saw the writing on the wall, and after a dispute with Ish-bosheth (king of Israel), he decided to go over to David to put and end to the war and bring peace to the nations. Yet Joab, David’s general, didn’t trust Abner and murdered him.
Notice David’s response: He gave honor to Abner to show them that it was not his plan to kill Abner, but to make peace with Israel through him. Also notice what he did not do: punish Joab. Part of the reason for the lack of punishment was that Joab was repaying Abner for the death of his brother Asahel. I also think part of the reason was an unwillingness on the part of David to discipline those who were his closest confidants. We see this even more later on in 2 Samuel.
This is once weak spot in David’s integrity. He punished the Amalekite that said he killed Saul, but not his friend that killed Abner. A person of integrity treats all the same, regardless of power, position, or prestige.