Sorry you didn't get a very nice doctor. I'm not trying to be a total pain here, but I would think a call to your rheumatologist MIGHT be a good thing, to ask about taking prednisone and what you can expect. And also about the wheelchair. I would think with a condition such as yours, they would be likely to allow you to purchase a wheelchair rather than ongoing rental.
When my neurologist sent me my prescription, I called my insurance and they gave me a phone number they said I had to call, the woman said this was the only place they deal with to get a wheelchair. It made no sense to me, I figured I could choose a place nearby to go with my prescription.

Anyway, I called the number and this woman starts taking my info. and says we can get you a rental by such and such a date, I said oh I'm sorry maybe I didn't explain well enough but I am purchasing a wheelchair, not renting. She was not very nice to begin with, but at this point in the converstaion her tone was she quite rude telling me we don't do that here, we do rentals so I can get you rental only. I said well unfortunately my condition is going to progress and NOT get any better, so a rental won't do me any good but you have a nice day! I called my insurance back and got a different person than I had spoken to the first time and she could not figure out why the first person even told me to call there.
Anyway, I know your trip is pretty close so you might just have enough time to do the rental and all but later on you might want to check into purchasing if your insurance will do it. I don't understand their logic in the cost, but that's insurance for ya.
GOOD LUCK no matter what, hope your trip planning is going well and that you and your family have a wonderful trip!