The best way to deal with this is to plan on a minimum of 30 days no contact. Do not call, do not text, in fact, avoid all contact not associated with your children. And if you can avoid that all the better. Move on with your life with the expectation that you will not reconcile.
Move on with your life with no desire to reconcile. She has done too many bad things that are not worthy of your love and attention. She has lost you and you are now free to do all the things you did when you were single that you had given up to be married to her. And with that go out and have the time of your life. Live it up. Take up rugby. Buy a sports car. Start dating people. You will probably be amazed how quickly her divorced friends move in for the kill when they find out she is gone.
If she asks you about it, what business is it of hers what you do with your life? These are just friends, right? Respond with a blank confused look. If she asks anything, 'sorry I gotta go, I was just running out the door.' Any communication is the potential for her starting a relationship talk. She will probably only try to convince you how much she has changed and what she is willing to do to save the marriage or worse ask you to try marriage counselling. Too late, correct? Avoid all communication if possible.
You have the correct attitude right? That I have done everything to get through to you and save the marriage. You are impossible. This isn't working. I'm not sure I want to be married to you any longer. I care about you as the mother of our children but I'm not in love with you any more. In fact, I would go as far as when she actually able to track you down ask for a 3 month trial seperation to sort things out. Then one week into it tell her you are not in love with her and I think we should get divorced.
Thats a start. But first, lose the concern "I also believe that she is riddled with guilt and shame at how she is treating me and my boys." Who cares. These are things they try and make you think to win you back.
