I'm not going to drive my mother to her appointment
What is her reason for wanting to be driven to her appointments?
She is addicted to being driven around all the time.
I get that you may be really annoyed by having to drive her around all the time, but she needs you to do that. She may too ill to drive herself around so you have to respect that and help her out. She could get sicker if you don't.
Sick? I doubt it. She's just not that useful anymore anyway.
While you do want to be supportive of your family members, you also do not need to drive your mother around if she can drive herself. Let your mother know that you also have things that you need to do, and if she wants to get somewhere she is going to have to drive herself sometimes.