The good thing is you are getting through some important stuff here.
Don't tell you kids he left because of you. You don't know, you can tell them you don't know. I guess you might go so far as to say that he thought he needed to leave to be happy, but even that is putting words in his mouth. When it gets down to it, let them ask him why he left. (Don't tell them to ask him, but if you say you don't know, it's pretty clear where they have to go to find out.)
He isn't thinking clearly, but in his fog, asking how the kids are helps him to convince himself that he is a good father. He "knows" that if he asks that in a text, the answer will be "fine", and he can go on with his life. Anything you say that messes up his plan will backfire, even if it is true. Because it comes from you. As he talks to the kids, eventually (and it could be a while) he will realize that they are not fine. And be prepared, because he will try to blame that on you. Since you must be telling them bad stuff about him, poinsoning their minds. And since he isn't there, if they are not fine it must be your fault! Don't expect that his logic is the same as a reasonable person!
The best thing you can do for your kids is to be there. Be the best mom you can be. Be strong and confident. Set a good example.
As far as H goes, I think the less contact you have, the better. It's hurting you. Remember that the person you can control here is you. Remember that your happiness is not up to anyone but you.
This is a rotten situation, but in the end you can grow from it, however it comes out. Don't let it beat you. Because you can control that, too!
