That depends on both you and him.
What your boyfriend did was an enormous betrayal of trust. I can't imagine what that must have been like emotionally. Being worried about him stabbing you in the back again is a perfectly human reaction, and his job is to demonstrate that it's not going to happen again. Part of that needs to be legal: If he's not already fully committed to child support, he needs to get on that horse.
You need to figure out, for yourself, if restoring that trust is possible. It might not be, for you personally. And that's okay. Relationships are built on trust and if you can't trust the person you're with, then the relationship is going to fall apart. It's better to figure this out now instead of dragging it out: That won't do you, him, or your children any favors.