Not sure about the loading/unloading on the plane/airport, but call your local airport and ask...and check with your airline.
Scooter Rentals...I rented one for the first time last May. I learned a lot! First rent one from a dealer that drops off at luggage services on Disney Property (I used ScooterBug). Second, get the INSURANCE...trust me on this...they are a lot harder to drive than they look (no brakes) and people step in front of you all the time! Before you all head anywhere, have her practice driving (include reversing) before you head anywhere. Know that there is a "switch" of sorts that puts it in neutral so that it can be moved without the key by just pushing. Buses...don't worry about what others think. Learn the magic words of I need help parking the scooter. Most bus drivers are extremely helpful...I did run into one that was downright hateful. But most were helpful. She will need to be able to drive the scooter onto the bus, most drivers will then help you park it. (some may ask you to get off and take the key and then move it in the neutral position to the parking spot. , some may just ask you to hold your hands close to your body and they will steer it while it is on.) Disney prefers for the rider to be off the scooter for the bus trip. I normally stayed on it if the bus was really crowded. Just seriously have her watch out for people that will just walk out in front of her...this totally amazed me! Bring her crutches along, as there are some places she will have to walk. No need for a special pass. There are procedures and/or spots for wheelchairs and scooters at every ride. Some may be to park the scooter outside and walk the entrance to the ramp (like Tower of Terror), some may give you a time to come back to the FP line (then they let you in a special entrance (Jungle Cruise), and some you can take the scooter in until you get on the ride/loading zone (Soarin). It just varies. Ask the first CM you see at the attraction to find out what you need to do.
lynn