A.,
I am so sorry this happened to you and your family. My heart goes out to you! I am certainly no expert on this so all I can do is give you my advice.
In an effort to save your marriage, you could ask him seek marriage counseling with you but from what you've said I'm guessing he won't want to.
If it's possible, maybe having the kids spend a couple two or three days with the grandparents wouldn't be a bad idea. That would give you a chance to sort things out, have a little time to yourself and to let out the emotions you're having not to mention talk with your husband without having to be careful about kids listening downstairs.
It sounds like his poor decisions have already affected your children greatly (not to mention you). I know you still love him A. but just because he has destroyed your marriage doesn't mean he has to destroy you and the kids' lives too. I know you have to be devastated and you have every right to be! This is one of those points in your life where you have to be as strong as you can for your children. They are counting on you.
Don't be afraid or ashamed to seek counseling to help you work through things. Even if he doesn't come with you. This exact situation happened to my friend. She is doing quite well now and is very happy. She loved her (then) husband too even after learning that he had cheated. Like she would say, I deserve to be with someone who loves me as much as I love them. I only say that to give you hope. I know in the moment it seems like your world is crashing down but you have to step back from the situation and think about how much live there is left to live.
This may sound silly, but don't underestimate the value of a nice long walk! Exercise can be very therapeutic sometimes!
I wish you the best!!!!!!!
H.