The big picture unfortunately is that my BF is seeing that his relationship with his brother needs major work.
Good. Now all you have to do, and it will be hard, is distance yourself from the situation between them as much as you can. Certainly listen to your BF, sympathize, be open with HIM, but when the two of you are not alone, just let the thing take its course. It will almost certainly become unpleasant, but it does not have anything to do with you, and the main thing you want to do is do or say nothing in the brother's presence that can give any of them, now or in the future, any reason to say that you had anything to do with what will undoubtedly escalate into a brother against brother "fight."
Because no matter how awful your BF feels now, or how justified his anger at his brother is and will be, it's still his brother, you are all I think very young, just starting your adult lives, and the brothers will eventually "make up" and this whole period will be a joke in 50 years.
And you don't know yet for sure that you will not be sitting there laughing with them, your old gray headed husband, and the man who will by that time be also YOUR old gray headed brother. (You, of course, will color your hair, and it will look fabulous)