He was married. In a marriage of convenience, a fact his wife was also aware of.
He had children. Definetely true.
He cheated on his marriage. We don't know on what terms of sexual exclusivity Elia and him were.
He knew his mother was being raped. By his own father who was also the king of a feudal monarchy. Older men were also aware and did nothing.
He knew his father was unstable. Yeah, so did everyone else. It's possible the tourney of Harrenhall was originally intended to solve that by Rhaegar's request. Which would also stopped the rape situation.
He knew Lyanna was bethrothed. In an arranged marriage her family wanted. He also probably knew she was not happy about it. His mother had not being happy about her own engagement. The marriage didn't turn out well, as you seem to have noticed.
He knew Lyanna was a child-woman. Of the same age his own mother had married and given birth to him which surprised no one within his culture.
He knew there was a war raging. We don't know when he came to know.
He knew Brandon and Rickard had been murdered. We don't know when he came to know.
He knew his whole family was unsafe. False. His wife and children had been left safe in Dragonstone.
He did nothing to ensure the safety of his discarded wife and children. At what point are you referring? She was first left safe in Dragonstone and then he could do nothing to solve the semi hostage situation.
He took the best fighters in the realm to Dorne to protect Lyanna leaving 16 year Jaime to protect his family. Should he have taken one of them with him so there was parity or we take into account Elia was also protected by a whole army?
You are missing exactly all the context and nuance the text provides plus you are missing coherence. If Rhaena being maritally raped was bad and he should have done something why should a situation where Lyanna was gonna be maritally raped have been accepted by him?