What is an appropriate role for a sibling who lives far away from an aging parent?

It is very odd, isn't it? I don't really understand your relatives' attitude either.

Is it at all possible to arrange a meeting with your siblings? And *only* to discuss the situation and how it can be improved? You could set an agenda for the subjects you would like to discuss eg
1. Travel costs/other costs on your family
2. Reasonable times/periods of time you can visit
3. What exactly your mother needs, and what she may be expected to need in future
4. How this can be covered
5. What you cannot do eg provide emergency cover

They could add their own suggestions.

This used to work really well for our family!

Thanks for your input. My mother lives the hometown she grew up in with loads of relatives around. I am basically the only relative who lives a long distance away. Her main health issues are just frailty from lack of exercise. The only health issue she has is high blood pressure. Her memory is probably better than mine. She loves being catered to and has spent over 20 years saying how incapable she is to doing anything and having others do for her. While I have generally driven to visit with her 2 and 3 times a year for the 26 years I have lived this long distance away, neither she nor my siblings have made the effort to drive to my home because "they can't". It is always expected that I am the one to conform to their needs. I did it for years, but I am aging myself and feel burnt out at this point. I do have resentment that the whole lot of them are more than willing for me to leave my own family and pets for extended periods and have no care for my life needs, just drop everything and come now. I have always been the one to sacrifice but no one acknowledges the hardship of it.
I am willing for my mother to come here for as long as she wishes but as one of my siblings told me yesterday, "no one is going to drive her there and no one ever will" and my mother says she can't come that far. I also believe that it isn't that difficult for her to sit in the car and ride here. She really doesn't have any special equipment except a walker and has bars around her bathtub. She doesn't have any nursing care because my siblings are tightfisted and don't want to spend any funds for any outside care. They expect that we should be doing it all with no help or expenditures. One of my siblings handles all her finances and doesn't share the information. I am expected to eat the expense for my travels to her house and home again, which is generally $200/gas while the sibling docks her accounts for any in home travel he does on her behalf.
There are a lot of issues here and resentments, as I see I am unloading all my frustrations here. I am suppose to go to do a turn to watch after my Mother in a little over a week and I am having second thoughts on whether to go, whether to just go, pack her in my car and drive back home with her, whether she agrees or not (is that legal?) and let her stay here while I am able to maintain my own life as well as care for her. The attitudes of my siblings who always make me feel like I am never doing enough, or how dare I not just drop everything and run to suit their schedules (one sibling is not responding to me now because I wouldn't come in a 2 day notice), make me not want to come to tread in hostile waters as well as neglecting my own responsibilities at home.
Again, thanks for your feedback.

As a full time caregiver for my mom, I gave up a place I loved to live in, a lifestyle I loved, my friends, my job, and my contributions to social security retirement to come back and care for my mom. I struggled with a huge amount of resentment toward my sister, who had been "taking care" of my mom, but not well. If you do as your siblings seem to expect, you will probably be angry and resentful the entire time you are with your mom, and that will do neither her nor you any good. Nor should you be expected to "abandon" your family.

Has she lived in her town for a long time? Perhaps she is concerned about losing support of or contact with friends/church/social organizations while she is gone? It's very difficult for the elderly to move to a strange environment and lose their social support. In that sense I can see her reluctance. On the other hand, if you have children, a supportive church or social organization that she could be included in, perhaps that would entice her? 400 miles is not that far to travel. Is your mother able to travel or is she incapacitated? Just how much care and/or medical equipment does she need? Would it be terribly difficult to transport equipment? Can you provide care in your home? Does she have visiting nurses where she is now, and could you get them where you are?