@Janabean427,
Decide whether you want to stay, and what will be best for your children.
If you need to stay, then things have got to change. That probably means couples counseling. Get it out in the open with an impartial third party observer about why this is such a serious problem. Maybe he needs to hear it from someone else who doesn't have a vested interest? I don't know. Certainly you two need to have a conversation about him being untrustworthy.
If you need to leave, then consider how you will afford that. It's possible, but the end of relationships often changes economic conditions, particularly for children. Hate to say it, but it's true. If that's okay, then by all means go. If it's not, then consider how to make it okay, whether that means taking a class to find a way to get a more lucrative job, or moving in with your folks if they are still alive, or sharing custody, or anything else. Breaking up when you have kids is a different ball of wax from breaking up when you don't, but it's not an impossibility.
I'm sorry this is happening.