Okay. Just read the thread. Yeah, fasten your seatbelt. I feel for you when you said that sometimes you feel like things will work out and other times you don't. You're going to feel a lot of different things. You're going to hear and read a lot of different things as well.
At the end of the day, you and your wife came together as a family for a variety of reasons. Divorce and separation are a lot easier to do when kids aren't involved but here's a truth you can verify for yourself... divorce rates are very high. If you leave, you have no guarantee that any of this gets better and in the meantime, your feelings and thoughts about the Affair will still be there.
I'm with Bandit on this one. You need to verify that she is telling the truth. As time passes with verified truth, you still won't trust her, but maybe you get to a place where the passage of time feels safe. The farther you get from her lying, the more clarity you and she will both have.
I didn't get to have any of that but I sure prayed for it. My verifications led to more bad stuff. I did the polygraph. We have a postnup now. The consequences and sacrifices to me personally have been brutal and I pray to God that someday I'll feel it was worth it. Amazingly, when I feel broken and spent and shattered into pieces, there is a resevoir inside that gets me to work that keeps me going. I have to believe that it means Something; if it means nothing at all then I chose to force it to mean that my daughters will have a normal childhood... and that got me through some very dark times.
My daughters were 9 and 5 when, in front of them, my wife demanded a divorce in response to my questioning some suspicious behaviors. They remember it, but both of them (like most kids) are surprisingly resilient. Even if it isn't safe, warm, and trusting with your spouse, if you can have it be that way between you and your kids, then at least they win. And, yes,... you'll choke on the hypocrisy of your wife spending quality time with the kids.
If nothing else, the most sensical thing I've seen on your thread is to verify what she is telling you about it. After that, don't victimize yourself by jumping to permanent and lasting decisions right now. Your wife wasn't thinking clearly about your family during her affair and - in a cruel twist of fate for you as the betrayed - your ability to think clearly is devastated. Give yourself time. Find a safe place. I have a few places that have always felt safe to me. I'm in such a place right now writing this. My wayward wife is revieiwing homework with my daughters. The youngest is riding her bike and I can hear her yelling to her sister from the street. The oldest is tattle telling because neither have practiced piano. For right now, I feel safe. My daughters don't know my wife cheated. This moment between them in a family that loves them would not be possible had I left 2 years ago.