Hello Quanticia: A bout with cancer can change everything. Although I've struggled secretly with mental health issues all of my life, my public downward spiral began following a bout with cancer. So I have some idea of what your mother has experienced.
It's so unfortunate your father & brother treat your mom the way they do. She needs support not abandonment & criticism. But, I have to say it is not your responsibility to save your family. I hope you know that. You have your own life to lead & falling into the trap of feeling like it's up to you to save the family can be the beginning of your own downward spiral.
Of course, I do understand you want to do what you can to help. I think the things you can do are to be present to talk with your mother about how she's feeling (both physically & mentally.) Perhaps you could take her out for an occasional walk or to lunch. Also, perhaps, if she has some interests such as cooking, gardening, or whatever, & you could share these with her.
I recall reading in a book by Parker J. Palmer where he wrote about a time in his own life when he was overwhelmed with depression. Nothing anyone could say or do seemed to help until a neighbor came over to visit. The neighbor massaged Palmer's feet & just spoke softly about how Palmer seemed to be doing that day. Palmer observed that this neighbor had found the only place left on Palmer's body where Palmer could still feel anything... his feet.
And while I'm on the subject of Parker J. Palmer, in another of Palmer's books, he writes about how one person can never truly understand what's going on inside another person. We're just too complex for that. As a result, all one person can do for another is to be present & to provide support for the person to heal herself. I believe this is true for your mother, & for your relationship with you mother, as well. Be present, be supportive, look for things you can do to support your mother. But, at the same time, understand it is not your job to heal the family, & you cannot heal your mother under any circumstances.
Oh... one more thought... one thing that might help would be if there were some kind of support group for cancer survivors, particularly breast cancer survivors. These kinds of opportunities can be wonderfully supportive & healing. And there might be opportunities for you to participate along with your mother as well. My best wishes to you...