Hi Christine, and welcome to A2K! I see you have only been here recently.
I can certainly appreciate your frusteration, and unfortunately, you have siblings that have decided to take a back seat to helping out your mother, since sis seems to be handling everything.
Does your mother not have any friends in her life that visit, and perhaps ocassionally help out? Or any alternative support network at all?
In what sort of housing does she live? House, townhouse, apartment, etc? Is she friendly with nearby neighbours at all?
Does the place where she lives offer any community services for seniors? If so, I would make some enquiries for information to see what kind of help may be appropriate for her.
All this would be an effort to lessen the burden on your shoulders, at least occasionally, to give you a break.
Either that, or it may be necessary to have a "tough talk" with your mother to say that you're sorry, but you're just unable to always be there when she wants you to.
A lot will depend on her financial situation. In other words, would she be able to afford to take the occasional taxi when you can't drive her to an appointment (or whatever)?