Welcome to disABILITIES.
You've already gotten some good info; I'll just add a bit.
For the refrigerators, calling Special Reservations is your best bet. Whether you will get the $10 fee waived or not is anyone's guess. They used to always provide a free frig for people who needed it for medications. Then about 2 years ago, a lot of people posted that they were charged. Some had even gone thru the Special Needs number. The reason given for still being charged was that so many people were
sayingthey had a special need for a refrigerator just to get one free. So, instead of sorting out who actually needed one, they just charged everyone. Recently people have been posting that they were not charged. Make sure your medication is clearly marked to indicate it needs refrigeration. mention your need again when you check in and check your statement when you check out carefully. If a charge appears, be ready to talk to the manager.
The Special Needs Reservation people should be able to direct you to the right place for cruise info too.
For the wheelchair/stroller question, as Poohnatic wrote, WDW rental strollers are large. They have 2 sizes and can accomidate up to a small 12 year old (at least that's what they say). The Studio has jogging type strollers (but with small swivel wheels in the front). The other parks have low to the ground, molded plastic types.
Here's a link to pictures on Deb's site. Her information and pictures are old (they DON"T still have the one front wheel jogging strollers at the Studio), but the strollers are similar. I don't know if your DD would be comfortable in these, but at least you can get an idea.
Of the rental places that Mike posted, Care, Colonial and Walker are full service medical supply places and should be able to provide a child wheelchair. I've been told that WDW has some child size wheelchairs, but they apparently are in short supply and I would not count on getting one. Some people just rent an adult wheelchair, but they are way too wide, the armrests usually are about shoulder height for kids and since the seat is too long, the kids end up with their legs sticking straight out (with nothing to support their feet) or they have to sit forward in the seat, so there is no back support. Not good situations for a child with RA.
A children's equipment company called
All About Kids rents children's wheelchairs and special needs strollers for bigger kids (sort of like larger size umbrella strollers, made for people 50 pounds and up). You might want to check on the Family Board to see who has rented stuff from them recently and how pleased they were.
Regular strollers are usually rated for a weight of up to about 30-40 pounds; these go up to 100 or 120. Any regular stroller you buy is also designed for a toddler; I have seen older kids in them, but they look pretty cramped and their legs are way to long for the stroller. Special needs strollers are expensive, but your insurance may pay most of the cost if your child's doctor writes a prescription for it.
You might want to check into renting a child's wheelchair or special needs stroller from your home area. That way, you would have it for the trip down - the walk thru the airport is pretty long. I would not suggest that for a
scooter (since if it runs into problems, you would need someone to fix it), but a manual wheelchair or large stroller should not be a problem.
Good luck and here's some pixie dust for a great trip.