Understand something about women... when you ask if it's "okay" to do something you know they don't like, and they say "sure", "if you really want to", "fine" or whatever... that is NOT permission... it's a DARE. If you go ahead and do it, it will dig in and take root in them and they will never forget it. They may forgive... maybe, but they will never forget. It will sit there like a grenade in their hidden arsenal, waiting to be rolled out under your feet should they feel the need. It can be years later; many years... but they can recall it instantly in detail you yourself can't even remember.
If you ask them to pick up something at the store they'll come home from the store without it having forgot you even asked. But years later they can instantly remember everything you did that they said was "fine" at the time. Women are strange creatures; lovable most of the time; some of the time. They always talk about wanting communication but never tell you a damned thing when you ask; you're just supposed "to know".
Don't live your life for her; do what's right and honorable for yourself and your kids. She's got that other guy in her life and did before you separated. It was her way of "showing you how it feels". She's still in self-righteous "justice and vengeance" mode. She believes you've been doing what she's doing, so in her mind she's fully justified in doing what she's doing.
You may never get her back; be prepared for that. Don't live for the possibility she may come back. Don't live to prove anything, just live to be a good man and a good father. Be nice towards her, be kind, be good. She may or may not deserve that but that's not why you do it; you do it because it's good for you to be that kind of person. Keeps you clean inside with your light on, instead of dark and full of bad things.
Change up some things; get involved in your church social activities. Be active; don't just sit around thinking about it or the past. Work on modding your car. Remodel the house; repaint; re-landscape; do something creative you enjoy. And pray that God do what's best for you, your kids, and her. And then live your life; you'll be fine.