Did you make it clear that this is NOT about you and her but about the welfare of your kids?
IMO you need to stop thinking about your M and focus on the kids exclusively.
Stop acting like she is a victim to this guy. I get her hooking up with someone and you have NO say over that, period. But, the kids are your domain.
I understand your worry. The fear of divorce hangs over you, believe me I relate but you've got to face reality here.
Again- “This is a very important lesson. You must never confuse faith that you will prevail in the end — which you can never afford to lose — with the discipline to confront the most brutal facts of your current reality, whatever they might be.”