My dad is like this. By this I mean a totally selfish arsehole who takes no responsibility for his own actions. Someone who can fuck up one family, then think everything is fine if he does a bit better looking after the second family. As if that makes everything hunky dory for the people he left behind.
I had very little contact with mine between the ages of 7 and 32. Had some contact as an adult to see if something could be re-established. No. He was still the same totally self-centred inconsiderate arse.
If someone genuinely has no ability to see how their actions affect others by the time they are properly an adult (25-30), then I don't think they ever see that, short of some "A Christmas Carol" type epiphany, which is really rare.
So, I think you give up on it. The thing about writing a card to apologise is pretty fucked up- sounds like he cares a lot about his own feelings, no-one else's.
He was bad to your mum, you saw that, it can't be undone. Now he is bad to you. He isn't trying to make amends, or build something positive, just making you jump through hoops so he doesn't have to confront his own bad behaviour and maybe feel bad or guilty about his past or current behaviour.
So just quietly do nothing to maintain the relationship. It is his loss not yours.