I'm sorry, it's just awful. Gut churningly horrible.
I wish I'd had MN when it happened to me, it might have saved me a hell of a lot of 'trying to sort it out/work it out'.
Just remember he will deny, minimise, eventually only admit what he knows you know...you can't believe a word that comes out of his mouth, even though you'll want to.
If I had my time over, I'd go and pack a bag for him, hand it to him and simply say 'You know why, don't even bother lying to me, just go. We can tell the children at the weekend, I'll call you to arrange a time'. Stay strong and don't budge. Everytime he goes to speak, just tell him you are not even remotely interested in anything he has to say right now.
It won't be easy, but holding onto your composure & dignity will mean a lot to YOU down the road.
You can fall apart AFTER he leaves x
...and for God sake, do NOTHING with regard to her. It might feel good for a short while, but that doesn't last. In the long run it's just humiliating and that's what YOU will remember. If I can't set a good example, please let me be a warning! X