Forget about getting back together with her right now. You need to talk to her to get rid of the tension right now between the two of you because your sons are suffering because of them.
Take charge, tell her you did not appreciate her infidelity and blaming you all the months while she was doing it and that all of that would be handled by your L's. You are now interested in your sons' well being and want to be sure they come out of this as unharmed as possible. Call her out on her crap of not showing up for the games, etc. Again this is about them not you and her. Stick to that.
Whether you want to press for the D or not, that's up to you. You were betrayed and want her to pay. I totally get that. To this day my W has never shown any regret or remorse. In that survivinginfidelity website, I learned alot about the triggers that would set me off and how my reactions were totally natural. Face up to your own feelings rather than "blaming" yourself for things.
Eventually you will have to coparent with your W. Think of it that way. Put the welfare of your kids first. They may need C. If your W disagrees, then you have to be at a comfortable enough place with her to debate her about it.
Right now I see them being stuck in a tug of war between you two. Man-up, grow-up even if she doesn't want to.
M-43 W-40 2D - 9 and 5
Emotion, yet peace. Ignorance, yet knowledge. Passion, yet serenity. Chaos, yet harmony. Death, yet a new life.