David is unwittingly involved in the set-up, by agreeing to Amnon's request to have Tamar make him some cakes. II Samuel 13:6,7.
He KNEW what happened next, and was very angry. II Samuel 13:21.
He did nothing for two full years. II Samuel 13:23.
The death of Amnon comforted him. II Samuel 13:23. (I THINK that's what this verse means, but there may be some other meaning I'm not seeing.)
Is it because Amnon was David's first-born son (II Samuel 3:2), and perhaps heir apparent?
With respect to the heir apparent, I'm not entirely at ease about that argument. So far, the Kingship has not followed bloodlines strictly:
Both Saul and David derived their crown from Samuel (I Samuel 10, I Samuel 16);
It took the intervention of Abner to put Ish-bosheth, the son of Saul, on the throne of Israel.
It sure was confusing when the kingship was actually transferred (II Kings 1). Chileab, David's second-born, is never mentioned after his birth is noted (II Sam 3).
Solomon, David's designated heir, was son number 10 from wife number 8, if I am recording things accurately.
So, I SUPPOSE the idea of the kingship passing to the oldest son could have been strongly favored, based on the traditions of other kingdoms, but was it strong enough to keep King David from disciplining Amnon for raping and rejecting Tamar?