First, WOW. I'm so sorry that you are going through this.
My parents have issues, but I can definitely see why you are so overwhelmed.
First, with your brother, I would call him and ask if work is really why he doesn't talk with your mom. Ask him if he would call once a month (and like the PP said, space your calls out monthly, so that there is a check in).
Second, with your mom, you are going to have to cut back. I know you love her. Of course you do. The fact of the matter is, she is hurting herself. She is in an unhealthy relationship, she is also very unhealthy herself. If she were the alcoholic, you would do anything to stop her from drinking. I guess before you leave, I would tell her that you need to talk to her about it. And then try. Tell her why YOU feel she needs savings, to lose weight, and that YOU are afraid of losing her.
There is medicaid, and Obamacare is coming, so if something happens, you wouldn't be responisble.
You need to focus on your journey. I know that you aren't the only ones, My husband's father is not very responsible. He is very dificult to deal with at times.