Okay, breathe. You are seeing each other and the kids, so there are positives right now. Willingness to spend some time with you. You contacted a therapist. This is not going to resolve overnight because it did not happen overnight, so give things a chance to settle down a bit, okay?
Stop the pity party that you cannot compete with this guy. Says who? Just you? Please have more faith in yourself than that. So she had a fling, , forgive her AND yourself and keep moving forward. Things have been so tortured for the past two weeks that some dust has to settle, so let it. BREATHE, GO FIND A FRIEND AND GO BLOW OFF SOME STEAM!!!!! You need it.
At least your W is talking to you. My H is not doing anything, which is ticking me off. Oh, well, nothing new.