I feel like I would be selfish and betraying the kids if I weren't to give things another shot.
How many times have you caught him cheating on you?
That's probably less times than he actually has cheated on you.
You've given him all those chances/shots.
Many a person would have been out at the first cheating episode. And they'd be 100% justified in that.
Cheating is a type of abuse. You are not the best, happiest, most relaxed, most confident, most centred etc you when you are being cheated on; that includes you as a Mum. So it's not actually in your kids best interests to stay with a serial cheater, while he's doing or or even after he's done it and is pressuring you to reconcile/stay together. As you say, it's too much damage to recover from.
You and your life are not a sacrifice for your kids.
And you're not your best and happiest self for them with a cheater either.
People break up and coparent every day of the week. Half or more of the kids at my Lo's school are from blended families.
You are not failing them, he failed them. You did nothing wrong in the marriage, you stuck to the agreement, he did not - repeatedly.