A family is like a mini-society. There can be problems between family members, and when this happens it is the responsibility of the parents to function as the government of that society and correct what needs to be corrected.
David had several wives, and Amnon and Tamar did not have the same mother. David was the father of both of them, and it was clearly his responsibility to correct Amnon, to do what was necessary to set the situation right. Perhaps he could have forced Amnon to marry Tamar, which would have been acceptable in those days.
The Scripture tells us that David heard what had happened, so he could not claim that he did not know about it. David was understandably greatly angered by what he heard, and yet as far as we know, David did nothing at all about it. His oldest son had committed an awful sin against his sister. He had essentially ruined her life. She lived the rest of her life sad and lonely in the home of her full brother Absalom. No one would marry her now.
And yet David just got angry and did nothing.
Parents have a God-given responsibility to see that the family functions in an atmosphere of love. They are also the ones who should be teaching their children that there is justice in society. Tamar had lost all respect for Amnon. What is probably worse, she must have lost respect for her father David. And because justice ultimately comes from God, David's failure to administer justice in his family probably distorted Tamar's image of God's justice.
May God help us as parents to exercise our authority in an atmosphere of love and in a way that demonstrates to our children that God loves them and will see that justice is done.