It depends on what’s your bottom line. For me, cheating is a no. If he loved you and the family enough, he wouldn’t have cheated on you regardless 10 years ago or now.
My bil cheated on my sister twice during their marriage and despite asking for a last chance just 2 years back, he cheated again a few months back. It takes a cheater to stop a cheater (Don’t get me wrong, I’m not asking you to cheat. It’s just that I feel you’re probably not the one that would make him change for good judging from what he has done to you.)
Do you have any family members you can turn to for assistance? Like to help out with your kids while you work or when you need to leave work later on certain days.
End of the day, please make the decision for yourself and not for your kids. It will be hard, but you’ll brave thru this. I personally didn’t forgive my mum for cheating on my dad (thrice) and im glad he found someone better for him.