If it were me, I wouldn't want to live in it, either. I don't think you could make a decision or act upon a promise she makes of never doing it again. At the time she makes the promise, she probably has sincere intentions. However, this is a problem she has not learned how to manage. Promises mean little when it comes to things we don't know how to control.
I think she would need to stay under the care of a therapist (or whoever deals with uncontrolled behavior problems), at least go to an anger management program. If it were me, I would have to see her stick with improved changes.......when she was around you. The relationship would need to merge slowly, for both of you to feel safe with each other.
I also believe both of you need to take classes in how to communicate within a personal relationship. If you have never studied material on the subject, you could be doing that while S from her. Sharpen those skills so that when you do talk with her, you will be better prepared.
It wouldn't hurt for you to see a therapist to see why yelling affects you to the degree it does. I hate, too. I did not grow up around it and there has been no screaming and yelling in my M. I have seen little children almost go into a spasm out of fear of an adult yelling/screaming angrily. It's nothing to take lightly.
Has she ever said if her anger issue was the cause of her other divorces?
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!