So I'm going to play devil's advocate. People fuck up. Couples can come back from cheating. There is a great TED talk on it, if you want to listen to it. Whilst cheating is a horrible thing to do to a person, people make mistakes, and how they deal with their mistakes, is often a better tell of the sort of person they are than the mistake they made.

But you both need to want it, you both need to work REALLY hard. This is a great time to air all your grieviences and really communicate, no holds barred. You don't have to decide now. You can take how ever long you need to calm down and make a calm decision.

Though the fact that he was caught, and didn't divulge the information of his own free will, really counts against him as far as I'm concerned. I'm sure that there are avenues for you to follow if you decide to leave. I left my ex 18 months ago with our 5yo twins, it has been EXTREMELY hard, and whilst I watch him live very comfortably, I struggle every day, but there is rarely a day when I don't think it's worth it.