The dinner (and any food and beverage en route) is in gratitude for the time she is investing in this task for you. I still think it is appropriate for you to fill the tank at the outset, during (if needed) and at the end of the trip. As I said before, this would be the “ideal”.
The reality is that if you were able to drive yourself, you would incur those costs yourself. If you were paying a livery service to transport you or bus fare, those fees would cover the cost of the fuel for the trip and the wear and tear on the vehicle and the salary of the driver and may well exceed the cost of covering all her expenses as I noted (in addition to probably taking more of your own time in the process). I raised my son to cover his own expenses in such situations and to negotiate how such things would be handled before the trip commences in order to avoid conflict along the way.
On the other hand, if I had someone I was close to that relied on me for transportation, I probably wouldn’t ask for any reimbursement, unless I was pretty broke to begin with. I don’t know the nature of your relationship with your sister, and that seems to be a big part of the issue here, since you state that she’d suggest a very high amount, it seems she may harbor some resentments about feeling imposed upon or under-appreciated. Perhaps you could provide more details in that regard to help us help you figure out what would be a compromise.