Sorry, maybe I didn't explain it well. All parks have trams that service the regular parking lots only. None of the parks have trams that go into the handicapped parking lots. I just talked about MK, because I had an expecially bad experience there, but the situation is the same in all the parks. The trams don't go into the hp lots because they can't accomodate wheelchairs &
ECV's. Your best bet is to use the regular parking lots. If you have a permit, the cm will let you park in areas in the regular lots that are closer to the parks. I don't believe they have a sign, just have to be directed there by a cm. Or you could just let your daughter off close to a tram stop (ask a cm, I believe they have signs), then park and come back to join her. I assume she can stand for several minutes?
Also, make sure you get a Guest Assistance Pass. It won't help you with parking, but it does allow you easier access to rides, etc. It does not allow you to go to the head of the line, but in your daughter's case it will allow to use alternative entrances that are easier to navigate, such as no stairs, etc. You can get a GAC at the City Hall in MK, and various other places around Disney (maybe ask at your hotel if you're staying onsite). You can also use it for preferential seating at the parades--they have certain areas roped off for people with disabilities. There's seating there, they don't expect everyone with a disability to use a wheelchair. Its too bad the search function is down on this board--there's a ton of information for people with disabilities. Make sure to ask for Disney's guide booklet for people with disabilities. You can get it wherever you get your GAC or I think they will mail you one. However, its heavily slanted towards wheelchair users. However, you can get some good tips from it. Just take it slow, rest a lot, and realize you can't see and do everything (who does?) As long as you enjoy the things you do see, you will have a great trip!
A few more suggestions for your child with RA--is it possible to increase her meds while on the trip? Maybe talk to your Dr--I usually increase my prednisone by 5 mg more just while on the trip. It helps. Also, I've taken to using a cane in recent years. I find it helps with balance, etc., but I also find it serves as a visual cue to people that I'm not just walking slow, I do have a disability. I'm 50 years old, but I donn't know how a young girl would feel about using a cane. Most people her age are very sensitive to their appearance and would rather die than "look different". However, its just a suggestion that you might consider. Good luck and have a great trip!