She absolutely needs to stop talking to the OM. That is step one in any process to get a marriage back on track. If she doesn't want a divorce, she needs to do that. She also needs to get away from him because he is such bad news, even if they were just friends, given her previous behavior.
Let her know how encouraged you are by her improvements but do not back down on your demand that she stop all contact with him.
Good luck and stay doing what you can do for the kids. Now that school is going to start soon, you may want to let the teachers and school counselor know the situation, just in case the kids seem off during the school day. There are a lot of resources available to them to help the kids through any kind of traumatic experience.
Me: 34 H: 34 S: 8 D: 5 M: 10 yrs T: 12 yrs Affair: 7-1-10 (lasted 2 months, I caught him by reading emails, there was no sign of stopping until I caught him) S: 7-16-10