Hard situation man. I don't really know what to say to you.
Did the conversation between both of you felt sincere? If you trust what she's saying maybe you don't need to move out. Now that you know the problem you can both work together to fix it.
You seem to have a good family, 2 kids that would be devastated if you decide to distance yourself. If you feel there's the slimmest chance of things working out at least give it a try.
I know that you must be feeling betrayed that she was talking to him behind your back, but (if she's being sincere) she wanted someone trustful to listen to her problems. Now it's time to reunite and fight for your marriage, show that your the guy that she can look for when she's feeling insecure.
Your situation is one more remainder of how we, that have relationships, need to be more alert of how we spent the time with our partners/family. It's good to have personal hobbies, but the time together is very important too.
I, personally, have been working too much this past months. Never get to bed with the wife and always get up when she's already gone, I can feel that this is slowing detracting from our relationship.