In this chapter, Amnon rapes his half-sister Tamar, and Absalom kills Amnon in revenge.
In previous chapters, I have discussed David's character. What stood out to me the most about him is that he sincerely loves God, and he is capable of being very shrewd in terms of political maneuvering, but he is not a strong ruler in terms of controlling the kingdom and maintaining authority over his subordinates. This showed up most clearly when David did not take revenge on Joab after Joab murdered Abner. In that case, David depends so heavily on Joab that he simply cannot punish him for his clearly evil deeds. Again, in 2 Samuel 12, Joab overthrew the city of Rabbah, and only after the battle was nearly over did David come in to claim the victory.
In this chapter, what we see is that David shows the same weakness when dealing with his own family, and this is going to cause David a lot of problems during the remainder of his lifetime, perhaps more than any other issue.
Also, these problems are what Nathan prophesied about when he said that David would face evil coming from his own household and family, so it is indirectly the result of his adultery with Bathsheba.
Anyway, to establish the main players here, let us begin by observing that Absalom and Tamar are full siblings, the children of the same mother. Amnon is their half-brother because he is the son of David, but not the son of the same wife of David as Absalom and Tamar. Jonadab is their cousin, the son of Shimeah who is a brother of David. I think it is also significant that Amnon is David's firstborn, which means that he is first in line for inheriting David's throne. I think it is likely that at least some part of David's weakness in dealing with Amnon is that David expect Amnon to inherit his kingdom.
What happens is Jonadab (for whatever reason) tells Amnon how he can trick Tamar into entering his house, and then rape her. David unwittingly plays along the entire time, and at no point does he proactively do anything to control his children. I think if there's one thing that stands out to me more than nearly anything else, it's David's passivity in this chapter. He's angry sometimes, he weeps other times, but at no point does he do anything. And we're talking about the king, so he is supposed to be the supreme authority over the entire kingdom, and much more so his own family of which he is the patriarch. This lackadaisical attitude is entirely out of keeping with David's many responsibilities.
After Amnon rapes Tamar, it says that he hates her with a greater hatred than his previous love for her. This is, no doubt, because Amnon never loved her. It was lust, pure and simple and evil, and once he got what he wanted, his disrespect for her came out to the fore.
A couple comments. First of all, the law forbids sexual relations between half-siblings (Lev 18:11), so what Amnon is doing is at least forbidden, possibly punishable by death. Rape is certainly punishable by death. Secondly, in v. 13 Tamar begs for Amnon to marry her instead of raping her, but he refuses, and then he throws her out. To a significant extent, men would only marry virgins in Israelite society (and most other societies in the ancient world), so by having sex with her and throwing her out, Amnon is coming about as close as he can get to preventing her from ever marrying, which is one of the biggest events for women in this time period (more so than in modern life, though marriage is still obviously significant in modern life as well).
Simply put, sexual standards were a lot stricter for women in Israel than they are in modern Western civilization. In modern times, a woman could have a career, sleep with one or more partners, get married late or never get married at all. In ancient Israel, they did not have most of these options. Men in ancient Israel could have multiple wives, could have sex before marriage (with certain limits) and in broad terms, there simply wasn't any notion of male virginity in the same way that their society thought about female virginity. As a result, what Amnon does is possibly even more horrible than when a woman is raped in modern life, because as we can see in v. 20, this event is essentially the end of Tamar's life as she remains in her brother's household and is "desolate" for the rest of her life.
Third, when Tamar tells Amnon that his actions would make him a "fool", and that he would be doing a "disgraceful thing". The root Hebrew word for both of these terms is "nabal", which means fool. This is, once again, David's karma. Because of David's sin, he who once showed himself superior to Nabal, the fool, now has his sons acting like fools as punishment for his affair with Bathsheba. The repeated use of the word "fool" is meant to contrast the shift in David's affair before and after he commits his great sin.
Two people hear about what happened: Absalom and David. David gets angry, but Absalom gets revenge. This is what I mean about David's weakness. Because he refused to take action against his own son, he essentially forces Absalom to get revenge for his sister. By all rights, Amnon deserved to die, and David is the authority most responsible for carrying out justice, which he does not do.
When Absalom sees that David is doing nothing, he holds a sheepshearing celebration (similar to 1 Samuel 25), and connives to invite all of David's sons, specifically requesting Amnon to come. David once again shows his passivity by asking, why Amnon? But then permitting him to go.
David first mourns for the death of Amnon, and then eventually mourns for his separation from Absalom, because Absalom was driven into exile. Absalom flees to Geshur, because he is the grandson of the king of Geshur (through his mother, the daughter of the king of Geshur). Absalom correctly believes that he can find shelter from retribution there. It's sadly ironic that Absalom has to go into exile when he is simply carrying out justice, because Amnon deserved to die from his crime.
What we see is that David is starting to show the same weakness towards Absalom that he showed towards Amnon. Even though David made a mistake by not punishing Amnon, he is showing further vulnerability by not controlling Absalom too. This will come back to cause him serious problems in the very near future.