I need you to give up act 2 before I can start to fix what was wrong with act 1. She, though, has seemed to think I needed to show her something that would make her believe things would be different-in other words, fix act 1 before she would give up act 2.
OK, here's the distinction, Kartman:
YES, you do need to demonstrate to her that you "get it" -- your role in the dysfunction in your marriage, prior to her affair. You need to admit where you went wrong, acknowledge it, and demonstrate that you "get it" and are working on those issues . . . to become a better Kartman.
And then, whether or not those improvements -- the "new Kartman" -- get to be with HER, is COMPLETELY UP TO HER, and the decision she makes about whether or not to end her affair!
In other words, YES, she sees some hope, that things will be different. But she sees that hope in the changes you are making FOR YOURSELF, and in your mature acknowledgement to her that you have made mistakes in your marriage. But that awareness is a completely separate issue from HER DECISION.
Her decision is one of basic fidelity: will you honor our marriage vows, and come back and work on our marriage with me, or won't you?
So she can wait to SEE the changes you are making -- but she needs to know that that comes with a risk, and that is that you may lose what is left of your love for her while she tarries. Or, she can COMMIT NOW, end her affair, come back and work on the marriage with you.
"Sorry dear, that's a beautiful and heartfelt letter, but the ball is STILL in your court. That's just the way it is."