His responsibility for supporting his child does not depend on whether you are "nice" to him. He may have the right to have some input into the child's choice of college, but if he is difficult, you can go back to court to enforce the support order.
If you ever want peace in your life, I suggest you avoid all unnecessary contact with him. I understand that it would be nice to be "friendly" for the sake of the kids, but he's the one making that impossible.
He can't manipulate you if you refuse to play.