Hi and welcome to disABILITIES!
Each of the parks has a staffed First Aid location where a person can rest if necessary. Also I would suggest some 20+ minute shows in the parks, American Adventure in Epcot, Hall of Presidents or Country Bear Jamboree in MK or Great Movie ride at MGM.
Actually, you probably mean an Electric Convenience Vehicle (
ECV) which can be rented in the parks or from off-site vendors and streers with a handlebar like a bicycle. An electric wheelchair (usually referred to as a power chair) uses a joystick for steering and is usually rented only to people who already own them and can provide control setting information.
If you click on "disABILTIES" at the top of this page and look at the index, a few items down you will see the "disABILITIES FAQ" which can answer many of your questions.
One last thing, please ask your mother the following questions. Here are the suggested answers to go with them.
1. Are you disabled (even temporarily)? Yes.
2. Do the people you are travelling with, such as your family, know you are disabled? Yes.
3. Do you expect to meet anyone you know during this trip who may not know you are disabled. Probably No!
4. Do you expect to meet a bunch of people who you will probably never meet again in your life? Probably yes!
5. Is there any reason at all that you should care what these people think about you? Absolutely No!!
6. Will using a wheelchair or ECV make for a better vacation for you and your family? Absolutely YES!
Mike