Totally understand this, and you're not on your own. We have no contact with my family after years of conflict and haven't done for years, except after the the death of my parents. My wife is on a very low contact basis with her sisters, and has had to remove herself from them due to lots of issues.
We have one child, a son who is now adult and grown up, with a wonderful fiancée and a good life, apart from the fact that he is in Scotland (kids eh?), but he's happy and all that matters.
I worried too, about his future more than mine. He saw what was happening years ago, and hasn't had contact with cousins for a long time now, and it doesn't bother him. I'm more settled now I know that his future is looking good, with future in laws that love him to bits, and we love his fiancée as much.
I'd rather have a happy life than one that involves conflict and unnecessary drama.
I had to break the generational cycles and curse. It was hard, but so glad I did it.
If I have any advice, it would be to just enjoy your little family. Get the most out of each day and direct everything you have into that. It's often the case that 'happy families' aren't. My blood relatives seem to exist on alcohol as a common link. It's really not for me.