B, I hope your h is turning himself around...but don't put all of your eggs in one basket. Mlcers tend to break up and make up w/their affair partners many times over and if that doesn't work, they'll seek someone else out, especially if they've not finished up replay and depression.
If your h is closer to acceptance, he may very well take the necessary steps to heal himself. Like any addiction, he's going to have to wean himself off those "good feeling" kibbles and it will take a while to do so.
As for the calls and FB...she's trying to find out if he's back w/you. She's so transparent.
Take care of yourself and your boys. It's going to a bumpy ride for a bit, if he's truly done w/her.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.