Hello Tammy and thanks for asking the Disney Parks Moms Panel such an important question about your dear families upcoming magical visit to Walt Disney World Resort.
There's no getting away from it, there sure is a whole lot of walking to be done during a
regular Disney day so I'm thrilled to say that your darling Grandmother will, according to
Disney's Park Rules and Regulations be able to utilise her 3 wheeled mobility scooter - as long as it can maintain stability and balance when stopped, unpowered or unoccupied.
However you may wish to consider
Stroller Rental for your 2 young Mouseketeers as currently any trailer like object which is either towed or pushed is not permitted at Walt Disney World Resort. Double Strollers can be rented daily or for multi-day visits and can even be pre-paid for length of stay convenience!
To help plan your trip you might find this
Grandparents + Grandkids = A Grand Adventure link to be a super fun planning resource.
Have a great Disney day.
~ Jane