Well, I just started reading your sitch but I think you are way better off to be rid of him. Of course he's going to skew it when he tells the kids. Can't take any responsibility for problems. That is kind of why I was glad that I told mine alone after all was said and done.
Also, I would just talk to the kids when the times come up that present little teachable moments and let them know about relationships and how they are supposed to work.
Maybe when you meet someone great then they will get to see how it is really supposed to work. That is what happened with my kids. My S9 was old enough to know that his dad's and my relationship was NOT good. Even my d4 has started picking up on the truth about how her father is. He has shown them through his messed up actions and not being there for them.
My kids have so much fun with me and my bf and it is such a pleasant environment as opposed to what they WERE used to before. Your kids will see it in time, but I would take the chances to talk to them when they come up. No, don't tell them their father was a cheater, but he will probably show that in time to them as well. The truth comes out.
I teach 4th grade in a large Title I school around Dallas. Congrats on the job thing! I just found out I'm being moved to 5th next year (which has been out of control for the past several years!!!) so I'm trying to digest that.
"Success is the sum of small efforts, repeated day in and day out." Robert Collier
"One's best success often comes after their greatest disappointments." Henry Ward Beecher