I don't have any advice that others haven't given already, just wanted to congratulate you on this GIANT first step. A lot of women don't make it this far.
I would like to strongly agree on two thing and add one more. Legal representation, and documentation, very big! Plus, are there any witnesses to what's going on besides you and your kids? Friends, neighbors, family, maybe even his family? I know, the last one is not likely but I've heard it does happen. Have the cops been called to your house?
Any scrap you can bring to court will help. It's not fair, but you have to prove what's going on.
It might also help to do without childcare payments or alimony from him IF you end up getting full custody. Cut yourself and your kids off forever from this toxic person. But ask your lawyer of course, I'm not one.
And yes, he will do it to your kids and anyone else he can get away with. He's not a happy person and he'll take it out on whoever is around. By the way, this might be one of those situations where you're kids will be on your side. Kids aren't stupid and they'll resent him thinking they are, if not now, then later. Just make sure you keep your dignity. The kids WILL notice that contrast. Keep your head up and in the game.
Good luck and let us know how you're doing. -S. Kav