You are obsessing about changing a situation that you have little control of. You have done everything that you can to assure her that she is the woman that you want. You want to remain a couple and a family but she is not as sure as you are. You cannot force your will on her, that is not making good decisions by either one of you.
I just keep getting the feeling that the reason that this is going on is her refusal to make peace with the past, and she is giving you a taste of what happenned when things disintegrated between the two of you years ago. I might be totally off base here, but it may have taken her this long to follow this path. She has feelings for you but is not sure what they are right now. Don't force her into making a decision too quick. She may resent that, too.
I know that you don't know if you can trust her to give up the other guy, but sometimes you have to take that leap of faith. There was a deadline of Dec. 1st and she supposedly called him to end their affair. That should be encouraging to you.
She may not be able to jump into your arms right now, but at least she is willing to listen and to attend events with you. That is making an effort that you should encourage but not force. If you keep pushing so hard, it might backfire on you. Back off a bit and give her some breathing space. You want her to come back to you because she loves you, not because she is scared that you are stalking her. (Okay, stalking might be a bit strong, but do you see my point?)
Meet her at the playground with the kids, be gentle and try to let the anger of the situation out before you meet her. If you show up with anger, that can poison the entire encounter, and your girls don't deserve to see their parents like this.
Get into some counseling right away, both of you, either separately or together as you both need help to sort this situation out no matter what happens. You both need to talk to someone because the emotions are too raw.
She admits that she still sees you in her life, but her guard is up. If you back off, she might feel like letting her guard down some.
