So stop trying to win her back. Take the pressure off yourself and stop being tense.
Start right now simply working on yourself. Consentrate on a life with your kids and planning your future. You are right, if you don't make permanent changes, you will repeat all of this with another woman.
BTW, you have talked to a lawyer, right? If there's ever a time to stand up for yourself and your kids.......it's when the W is leaving you for OM!
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!