That was some great insight from the eyes of the kids, Joe, thanks for sharing that with her.
Shay, I'm so sorry! My husband and I had a rough spot, too, and I remember how scary it was thinking about starting over by myself pregnant with my third child. I was sitting in a battered women's shelter, because he hit me a few times at 7 months along. He was depressed, we were living with his mom, and things were pretty low. I thought our marriage was over, because who should stay with a man that would hit a woman when she's pregnant?? Whether he was just going through a temporary depression or not, I had to get out.
We did end up having a happy ending to our situation, and I would love that for you, too. However, that's not always the case.
My only advice is to throw yourself completely into God and being a single parent to your kids. I would consider counseling with a trusted pastor, teacher, etc... that can help you establish Godly boundaries. Because it sounds like if you do pick yourself up and move on, then your husband might try to do the whole come back to you thing again and just keep playing games.
I know Hosea in the old testament had a prostitute wife, and he took her back many times and gave her forgiveness many times. However, the difference is that God actually called him to marry her in the first place because it was supposed to represent his relationship with Israel and how God is continually forgiving His people.
Maybe God will call you to continually forgive your husband and to allow him to keep coming back into your home... but I don't think he's going to ask you to do that unless he has a great plan for how you are going to over come. I also think that God would make such a request very clear. If you have strong doubts, then I doubt whatever you are hearing is from God.
Biblically, I think it's ok to let him leave. He's not behaving like a follower of Christ, so I think you aren't sinning by letting him go and letting him end your marriage. So, that's not an issue.
Now, for the practical side of things.... Go ahead and establish child support. You can text him and ask him nicely if he wants to set up child support without involving the courts, or if he'd rather everything just be handled professionally. Don't fight with him, because I'm sure he won't respond the way you want him to, but I'd just tell him that you need help raising the kids and will be filing for child support in two weeks if he hasn't started support by then.
Be sure and not let him contact you just before two weeks is up and ask to start paying next month, he'll just be putting you off. Basically, be kind about it but have the thought in your mind of "show me the money".... LOL! Don't accept promises or future plans to pay.
He may ask about visitation and you can suggest he call you when he wants to stop by for dinner with the kids, and unless you think the kids are unsafe, you can set up a plan for visiting the kids at that time. If the kids are old enough for input, ask them how often they want to visit dad. Do they want to spend every other weekend with him? Do they not want an overnight, but maybe to spend an occasional Saturday with him? I would ask them these things openly and objectively right in front of him. If the kids are angry at him, he can hear why from their own mouths and you guys can work on that with them. Assure them that it's ok to be angry about the changes, but that he is their Dad and it's important to still care about each other.
It's not easy, but having these boundaries accomplished and things out in the open will give you the chance to know what to expect and to not be yanked back and forth or abused constantly with his blaming and guilting you.
I also think it's a good idea that you are doing... if he calls and wants to talk, set up a future time to talk (Call me Friday night at 7, and I'll make sure I'm available to talk.) One thing about this is, he has to make the commitment and follow through to call you back. This will prevent his getting emotional one night and the next day feel completely different. He can't jerk you around as much this way. If he doesn't call when he's supposed to, then the next time he "wants to talk," you can remind him of that and just say, "I'm willing to still have a talk sometime, but why don't you make sure that's what you want first."
In other words, be polite... pray for him, but let yourself move on!!! You might always have to have some kind of relationship with him, because of having kids by him, but you can start setting boundaries on that relationship.
Oh, and you might want to talk to a divorce lawyer. You want to be prepared for how he handles his affairs. I don't know how you will split up cars, bank accounts, houses, bills, etc... but being prepared helps him to not rake you over the coals. You don't want surprised. Most lawyers will give you a free initial consultation, so you don't need any money. And if you need legal help and can't afford it, it's possible you might be able to look up information on free legal aide in your town.
There are a lot of services available if you are struggling to make ends meet, but many of them rely on your filing for child support off the dad. They would expect him to fulfill his obligation to his kids, and if he doesn't, then they will go after him for it. I don't know much about it, but they have all these dead beat parent laws and such now.
God bless, hon, I'll pray God walks you through this. I know he will, but it's always nice to pray for it anyway.