First the good news. He has had a lot of things going on in his life. 3 tours in 4 years, a child who is dying, whatever else I missed or didn't mention. So at least there is some basis for his going over the deep end.
Now the bad news.
Lots of other people, yourself included, have gone through a lot of stuff, and are act responsibly. His actions are a choice, even if he is depresssed.
Think of it this way. He is sliding over a cliff. You threw him a rope, and have been holding on ever since his walking out on you. However, the weight of his problems and his bad choices are starting to pull you over with him. At some point, no matter how much you love him, you must let go and save yourself and your little ones.
I don't know how long you expect your younger child to be with you, but your older one will have enough adjustment when that time comes. Stop covering for Daddy. Tell them the truth, gently. Say that Daddy is having a lot of problems, and isn't able to be the sort of Daddy for them he'd like to be right now. He still loves them, but needs to work through these problems. In the meantime, you three are going to go on as a family to try to make things better for yourselves. They need the stability.
As for your husband, tell him that you are finished with the games. Suggest he go to the VA to get the help he needs, but not to call you for assistance until he has been clean and sober for 6 months, minimum. Continue to communicate with him as to how and what the children are doing, but refuse to allow him to drag you into a conversation about how you are or about how his life is going, other than what you need to know to keep your children safe. (If he's drinking and driving, for instance, you have valid cause to keep them home with you.)
A lot of men while breaking up with their women will use the one he's leaving as a relationship counsellor for the one he's leaving her for. Don't let him. If he tells you anything about his girlfriend(s), tell him you don't wish to discuss it, and hang up or shut the door. Do not grill the children about what he says or does, but allow them to volunteer whatever they like. Show interest, as in "Did you have fun with Daddy?" but not, "When did you go to bed? Where did he take you? Who was there?" etc.
He likely will grill the kids about you. You can't do anything about that. When he has an appointment to be with the kids, until he is reliable again, tell the kids, "Daddy plans to come get you on Saturday if he can." They'll still plan on him coming, but they won't think you've lied if he doesn't.
Finally, do not allow it to get physical again. You don't need an accidental pregnancy at this point. If and when he gets his act together, and only then, you can start dating again, just as you would date any man as a single mother. Don't let him sleep over, as the kids will think you are getting back together. Don't let him do anything in your presence which you wouldn't tolerate in your home, like heavy drinking in from of the kids or whatever.
Make the divorce final. Demand reasonable child support, and expect him to pay it. Apply for any benefits - SSI for the child, VA dependent benefits, food stamps, whatever, that you or the kids may be eligible for. Don't be ashamed to ask for help, even from the government. You've paid taxes and worked hard to earn the help.
Long answers to a long problem, I know. Good luck. You will need it.