If you try to "explain" things by correcting her account of the facts, then she will probably react badly. But you don't have to agree with her. She is going to see through her own eyes the way she wants, and she will try to justify her reasons in wanting out of the M. Unfortunately, having the anger issues you do, only helps her to make it sound believable to anyone who wants to side with her. The only defense you have about your part of the breakdown in the M is to prove you have changed. So far, you have good intentions, but it takes a lot of time to change lifelong behavior. You can do it, but right now she doesn't trust your good intentions to go any further.
You don't have to listen to her rave, especially if it triggers your anger. Just say good-bye and leave. But don't start explaining anything, b/c she is not in the place to hear it.
She doesn't want to feel bad over the EA, huh? Well, she should feel bad, b/c if she never feels badly for having the EA, then she will never feel remorse or humble enough to want you to forgive her...and that is important. Couples who try to reconcile without working through these steps, stand a,good chance of another A.
I'm not saying you should preach to her, punish her, guilt her, place blame, etc. But neither should you try to pretend she did nothing wrong.....just so she won't feel badly. Both of you have done damage. When and if she ever wants to talk about reconciling, then the issue of her A needs to be dealt with. If she truly wants the M, she will be willing to listen.
LBH'S try to talk the WAW out of D by hashing through the problems. Sounds logical, but you cannot reason with a WAW when her mind is messed up from an EA. I realize that is a scary feeling for you, but talking does not work at this time. A lot of time may need to pass before the talking will be productive. Sometimes, it takes a couples of years, or more, before reaching that place. And that is considering there is not a third party involved.
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!