RSF- You know that your marriage devolved due to both of your actions. You know that you aren't responsible for all of this. You know that you tried to take the bulk of your time apart to work on yourself and get your head straight. You also know that she chose to lean on another man to give her a sense of stability. I doubt this will pay off for her.
Everyone deserves forgiveness including you. You both do.
I think your mistake is that you make this all about you and her forgiving you. This is now about her trying to choose a path for herself that she thinks will bring her fulfillment. That's all. She could forgive you and stay with him. She could go back to you and never truly forgive you. There are so many possibilities.
Nothing points to this being an irreconcilable situation. Evidence points to this being a tricky situation that will take time.
If I were you I would work on forgiving her and yourself. Where is the tension and anger coming from if you blame yourself? Why wouldn't you say fair is fair and throw in the towel amicably? No. I think you are pissed that she isn't owning her part, that she seems to be punishing you and your kids for what you believe is forgivable and your M is salvageable.
Look at my sitch. Look at the fear and vulnerability and torment I go through when H comes closer...
Someone made a reference on another thread as to how you get a cat to come sit on your lap...a tentative cat. It takes a little time.
I think you want some stamp of ultimate objective consensus that it is over. No one can do that, not even a judge. It is irreconcilable if you say it is.
I think you should focus on a) diffusing your anger and forgiving her and yourself and b) the logistics of your side of the D
