My heart goes out to you. I have a child with autism, who is now in a group home, and so I went through something similar. I am also a Psychologist, so I have significant expertise in mental health and other related areas.
First, I would see if different meds can help her. Trying to get her to exercise is not an option, given that she would probably be unmotivated and uncooperative.
As for your own well-being, I would encourage you to try to get some in-home support services. All states have waiver monies, which pay for eldercare in the home. We had a CNA and several therapy assistants, who came in to work with my son over the years. Some did minor cleaning, if it was related to his care. Having someone come in to work with your mother would relieve you of changing some of her sheets, etc.
Finally, I would encourage you to get out and about and keep your own social network going. You cannot live your mother's life. You cannot make her decisions. She will not be the grandmother you had hoped she would be. In a way, she is like an adolescent now. She lives in your home but has certain rights and privileges, such as deciding how much to participate in the family. I'm sure you have friends, whose teens refuse to go on family outings and stay in their rooms for long periods. This is part of how they show their independence.
We cannot control others. We cannot make them who we want them to be. The best we can do is carve out a space for them in our lives and give them opportunities. If they do not take those opportunities, we may be disappointed. I have worked with many families, who have children with disabilities, and we all experience these feelings. In order to survive, we have to find the things we can control that make us happy and defend our own right to these things.
When my son lived with us, I managed to have a life by working part time, keeping my friendships active, going to church, and working out at the gym. I kept a regular schedule most days. I found that when I focussed on my own goals and interests my emotional state was better.
I hope these suggestions help a little.
Susan Parker