You shouldn’t miss the role of family in the monarchies of Saul and David. Abner, the head of Saul’s army was the brother of Saul’s father. Joab, the head of David’s army was the son of David’s sister, Zeruiah.
Though the Old Testament seems to be terribly patriarchal by modern standards, women were not without power. The fact that Joab’s father is never named (only his mother) might indicate that in that family, she was firmly in control. Connection with well-placed women could give a man right to position. If, for example, Abner really did have a relationship with Ish-Bosheth’s concubine, it would indicate an attempt by Abner to claim Ish-Bosheth’s throne. Ultimately, this is one of the reasons David asks that Michal be restored to him. Being married to the daughter of Saul would give him a claim on Saul’s throne. (You will see this again when Absolom sleeps with David’s concubines).
Two things stand out to me in chapter three: First, the violence. The civil war between the house of Saul and David has more in common with the worldly power struggles than with a holy Israel. But second is the sheer effrontery of Abner. He knew God promised Saul’s kingdom to David (3:10, 18). And yet, he led the opposition to David’s rule. Then, when his feelings were hurt, he went over to David’s side. David may have mourned the loss of Abner, but it is difficult not to believe that Abner got what he deserved. Abner was an incredibly strong person, physically and politically. He “ran” Israel. But he could not overcome the will of God.