I'm so sorry OP. I know exactly how you feel because this has also happened to me. The only difference being that my DH came and confessed that he had met somebody else.
He was cold and distant for a couple of months prior, barely registered that I was in the room, didn't seem to 'see' me really, wasn't loving as he had been before. I knew something was wrong long before he told me, I just wasn't certain what it was. He came up to me in the kitchen one morning when I was making breakfast and said these exact words to me "I think I'm in love with somebody else", I will never forget that moment as long as I live. It turned out he was having an 'emotional affair' with a woman at work. I remember saying "I thought you were different, one of the good guys, but you are just the same as all the rest of them", and him looking utterly ashamed and replying "So did I." I took my DD and went to stay with my parents for a few days, it was absolute hell. We spoke on the phone, I questioned him about what had gone on between them, he swore they hadn't slept together. I asked if they had kissed, he said no - but he hesitated before he answered, so I think that was a lie. He also revealed that she was expecting him to leave me for her, which also makes me seriously doubt that nothing had gone on between them physically, otherwise why would she think that?? The thing about it all was he was stressed at work, we had just moved house, we had a toddler, and he was already in a really dark place before she came along, I believe he was depressed (it runs in his family). I think the OW was a symptom of how he was already feeling, not the cause. After a truly hellish year of trying to get back on track with our marriage (and during which I came so very very close to walking out on him) he started to get back to his old self, she was history, he got a job elsewhere, and now 5 years later we are absolutely fine. I was eventually able to forgive and my trust for him returned, I felt I knew him better afterwards than I had before (the bad and the good), however - I will never never forget. And I'm not sure I will ever forgive something he said at the time which was that he "couldn't think about me and my feelings until he had sorted himself out first". It's amazing we are still together after it all tbh. But 2011 will go down as the worst year of my life without question, and it was my DH who put me there.
I truly understand how you are feeling OP. I wouldn't wish it on anybody. Whatever course of action you decide upon here (and you are the only one who can make that choice whether to stay or go), you WILL get through it and come out the other side stronger, even if it doesn't feel like it now. Put yourself and your children first. And in the meantime surround yourself with lots of support, IRL and on MN, whatever helps you. x x