Welcome to the place nobody ever wishes they will end up!
Everyone here is pro marriage and pro sanity! Your story is so predictable and so common. Every iota of it is familiar, so you are definitely not alone in grappling with this.
It sounds like your husband is gone and therefore the best thing you may be able to do here is to let him know that you have "let him go". There is a thread here by Gucci Loafer called "Setting them Free". It may be instructive reading for you at this point.Setting them free should really be called Setting Yourself Free beacuse it sets you free from many things, especially from the potential loss of sanity (which must be avoided at all costs).
In a sense you are lucky that he has moved out because it will allow you to detach and focus on YOU and your children without his affair playing out before your eyes daily. This can be a gift if you choose to see it as such.
Your H may be gone now but he may come back. Just three days ago I ran into a couple where the H was involved with a much younger woman about two years ago. After it became too much, the W put him out and he moved in with the younger woman. Well, it took a while but he came back and after much counseling and work, they are back together. It CAN be done. It won't happen in all cases, obviously, but it is an encouraging story if you need one now.
I don't post much on the Boards now but I will drop back in to seehow you are doing. You will get lots of helpful advice here. Weekends are usually slow but once the weekend is over things will pick up and you will get several responses.