I still don't get why Jack is so horrified at having to maybe raise his nephew?
When they come back Jack isn't horrified. He is with Kate and Aaron at Christian's Eulogy.
Than Claire's mother shows up. Jack realises that Claire is his sister and Aaron is his nephew and that Claire's mom is the lover of his father. That changes everything.
Jack betrayed his father in the hospital, because Jack needed to tell the truth. He always wants to do what is good. His father lost his job and went to Australia and died.
The only good thing he can do now towards his sister Claire (who surely wants her mother to raise Aaron. She left her mother half dead in Australia after a caraccident and a fight and had never the chance to say sorry), and his father (who died, because of Jack wanting to tell the truth) and Aaron is telling the truth again and telling Claire's mother about Claire and Aaron. But he can't do that, because it would bring Kate in big trouble at the trial and it would blow up the coverupstory.
He chooses for Kate and he betrays Claire and Christian again.
I don't think Jack has a problem with Aaron, but everytime he sees him with Kate, he feels guilty towards his father, his sister, Claire's mother and his own mother and when Aaron starts growing and talking and asking questions he will have to lie to him too, every day. I don't think that is the father/son relation he has in mind.