IMO, the first book to read is NOT "Just Friends" by Shirley Glass, and I urge you to read that as soon as you can.
You ask 'How will I ever move on?' Alas, it's up to you. My reco is to stop, detach a bit, and look within yourself. My bet is that you'll find strengths that you didn't know or that you forgot you have. You really have the power to heal yourself, although healing may go more smoothly if you work with a good IC. From what you've written, I recommend a good IC.
I'm really sorry you're going through this. I urge you to remember, though, that you can still live a good life. Your W betrayed you, but that's because of her issues, not because of issues with you or your M. She failed. You didn't.
R(econciliation) is a much different matter. It's possible, but only if the WS and BS both do the necessary work. That means you don't have to R. That means not even trying to R unless your WS does her work - and that starts with coming clean.
Once she does that, you know more about what you have to deal with, and you can choose between D & R more easily. though it's rarely easy. If you choose R, you monitor yourself and your WS. If the WS doesn't meet your requirements, you can end R.
You're responsible for your self and, jointly, for your kids. You have to make your choices. Your WS is responsible for herself and, jointly, for the kids. For R to work, she has to change from cheater to good partner.
That starts with honesty, and your W is still being dishonest. One potential action is to tell her you're open to R, but only if she comes clean and agrees: no more lies, ever.
Also, As are hard to end if the aps see each other regularly, so I'd insist on finding a new job, away from om, and I'd insist on IC for your W, with a goal of changing from cheater to good partner.
But always remember: you need her if you R, but you don't need her to D. You can heal whichever way your M goes.