Added: I like what Veruca Salt says about not putting this on the kids (don't give them the decision). Not sure that you would, but that would be awful ... so hopefully they wouldn't perceive it in that way.
-----------------------------------------
Sounds to me - if you don't mind me saying - just based on this and your other questions - that your ex pushes your buttons.
Each one kind of starts the same - and to me, that means you need boundaries. Have you tried counseling, specifically in this area?
If your ex is toxic, and you see red when dealing with her (if she just drives you) and this is negatively affecting your parenting - then instead of bailing on the kids, learn how to stop this woman from affecting you. My husband was able, with help, to do this with his mother. Trust me, if he can, you can.
That's what I would recommend. It took a lot of work and me going with him, but he actually can deal with her without coming undone. He took her power away. I don't know your particulars and it's not right to compare, but honestly - just reading your posts, you sound upset still. I take it - it was a nasty breakup. Co-parenting sounds like a nightmare.
It doesn't have to be. You can have boundaries so that this doesn't get to you. It would be the biggest gift you can give to yourself, your wife, and your kids.
I would start there. If you decide to move, I think you'll need counseling to help you deal with those resulting emotions any how. That won't be easy. Parents sometimes have to out of circumstance. Doesn't mean they are bad parents. They have a lot of guilt as a result though - so at the very least, you might need help in dealing with that.