Hi Gretchen,
Our exciting to be sharing this trip with your grandmother. I also have taken my grandmother with us to Disney World a number of times. While she loves sharing in the memories with her great grandchildren, it is hard for her and her knees to keep up with us throughout the parks.
We have not had any problems being able to obtain an electric scooter for her use, however we are often there early. There is a limited number available, although I do not know what that number is and it seems to be quite high. It does seem from experience that the electric scooters go much faster at Magic Kingdom then the other parks There are of course manual wheelchairs for rent in the event the electric scooters are gone.
If you are not interested in using a manual wheelchair, and are concerned about the availability of the electric scooters, you may want to consider renting a scooter from a local company during your stay. There are a number of companies in the orlando area that you can contact and they will arrange for a scooter to be dropped off at your resort for her use. You can find a full listing by searching on Google for electric wheelchair rental in Orlando. While I have never used them myself, I have heard good things about
www.scootorlando.com or 866-778-4748.
Hope you and your grandmother have a magical time!