Much of the rest of 2 Samuel is the account of the chaos in David's household.  He who could rule a nation and defeat its enemies on all sides lost control of his own family.  We are not going to go into the details of these conflicts, except to say that they involved all the elements of David's sin with Bathsheba:  sexual aggression, faithlessness, betrayal, murder.  

        

There is not much good that one can say about David's son Absalom ("father of peace").  His grandfather was Talmai king of Geshur, a Canaanite region (located in modern Syria) that was not defeated by Joshua.  This means that David took at least one non-Israelite wife (Maacah).  Absalom got off to a bad start as the avenger of his sister's honor after she was raped by her half-brother Amnon (David's heir) (2 Sam 13).  David did not intervene to punish Amnon -- possibly because of his own guilt at having forced Bathsheba.  So Absalom brooded and planned for two years, then had his servants kill Amnon at a festival.  Absalom fled to his grandfather and stayed with him three years (2 Sam 13:37-38).
 
And yet David longed for him, for some reason -- certainly his affection was neither merited nor returned!  Joab acted as intermediary and got David to permit Absalom to come home, yet it was a strange rapprochement: Absalom was prohibited from seeing David in person (2 Sam 14).   Absalom continued in this state of domestic banishment for two years, before taking action to force David to confront him.  Typically for Absalom, he committed a rash and violent act -- the burning of Joab's barley field -- and, typically, he got away with it.  In fact, David kissed him (2 Sam 14:33).  
    
But Absalom was a schemer from long standing, and he despised his father.  This is evident not just from the conspiracy to overthrow the king, but from his following the counsel of the treacherous Ahithophel, who was probably Bathesheba's grandfather (2 Sam 11:3 and 2 Sam 23:34):

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         "Lie with your father's concubines whom he left to take care of the palace. Then all Israel will hear that you have made yourself a stench in your father's nostrils, and the hands of everyone with you will be strengthened" (2 Sam 16:21).  

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          This "advice" was not only to intended to humiliate David, but also to profane the Law:

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          "Do not have sexual relations with your father's wife; that would dishonor your father" (Lev 18:8).

         

David, as he retreated from Jerusalem, was joined by some foreign allies (or mercenaries?): Kerethites, Pelethites and 600 Gittites (2 Sam 15:18).  The precise identification of these groups is uncertain:  the Kerethites may have been Cretans, the Pelethites possibly Philistines. The Gittites were soldiers from Gath, where David had stayed for nearly two years in exile among the Philistines.  One of David's top three military leaders was Ittai the Gittite (2 Sam 18:2).  This shows that a considerable amount of "race-mixing" was going on, at least in the army.  The foreigners stayed loyal to David even when many Israelites did not.  We see the same thing when David reached his place of refuge at Mahanaim, across the Jordan:

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          When David came to Mahanaim, Shobi son of Nahash from Rabbah of the Ammonites, ...brought bedding and bowls and articles of pottery (2 Sam 17:27-28).

 

Incredibly, Shobi was the brother of Hanun, the Ammonite king that had insulted David's messengers and started the war between Israel and Ammon (2 Sam 10).  So an Ammonite prince was among those offering help to David at his lowest point!  And it was a Cushite who brought the news to David that Absalom had been killed (2 Sam 18:31-32).  The attitude of foreigners to him showed the evident respect in which he was held by the surrounding nations.

        

David never saw his son objectively.  He seemed incapable of understanding that Absalom was not just a personal threat, but an enemy of Israel itself, a perverter of justice (2 Sam 15:4-6) and a threat to the peace of the kingdom.  His mourning over Absalom's death was so excessive that Joab rebuked him for shaming his loyal troops who fought for him (2 Sam 19:5-7).  It is telling that the pragmatic Joab, who arranged for Absalom's return from exile, was the one who killed him, in defiance of David's orders.  He knew that Absalom was nothing but trouble, and if he wasn't killed he would continue to disrupt the Kingdom of Israel.