You really have two choices: wheelchair or
scooter.
With a wheelchair your mom can relax. She doesn't have the same concerns as with using a scooter. A wheelchair can fit on some rides like Universe of Energy at Epcot, a Small World at Magic Kingdom, Jungle Cruise in MK, The Great Movie Ride in DHS at Disney Hollywood Studios, Safari in Animal Kingdom, for example. These same rides do not except scooters on them. Some rides will allow you to go pretty close to the ride with a wheelchair and then the pusher can bring it to the safe zone. This is less walking for your mom. Also, you don't have to charge the battery on a wheelchair because there is no battery. A wheelchair would probably be more comfortable; because, you can elevate the leg. If your mom can and wants to walk a little to stretch then she can use the wheelchair as a walker. Finally, there would not be any problems with parking it like with a scooter on a bus. The downfall here is that you have to have a pusher for the wheelchair. If you have multiple people to push this might not be a bad alternative for your mom. I was in my early sixties pushing my mom in her 90s in a wheelchair at Disney over a week's time and I lived. It's doable.
With an outside vendor scooter rental you will pay more than for a wheelchair rental. With a scooter you are getting on and off the bus or other transportation and it's not easy to do it. You may need to use elevators at the resort; unless, you get a first floor room. To me it's harder getting on and off an elevator with a scooter than with a wheelchair. You need to recharge it and get the scooter in and out of your room each day. Some rides like Soarin' require you to use an elevator to get on the ground level of the ride to do it. It takes a lot more effort on the part of your mom to use a scooter than a wheelchair; because, she has to drive it.
Either way using a wheelchair or scooter I would concentrate on doing more shows and less rides. Keep in mind for shows, parades, and fireworks that you make sure you shut off the scooter when you are standing still. This will conserve the battery.
Pushing a wheelchair is a lot easier if you do rest periods with shows.
I think you should have your mom try a free scooter at the store like
Walmart, Target or wherever and see how she likes it. The scooter you rent will be better and easier than the one at a store. Also, I would approach her on using a wheelchair instead and see what she wants to do.