Here are some options:
Rent, borrow or buy a wheelchair in her home location and bring it with you.
If you rent one from home, let the company know you plan to travel. Buying an inexpensive wheelchair is a good option and might be no more expensive than a few days rent. You can find inexpensive models at places like Walmart, Costco and many pharmacies. If you don't need it after the trip, you can sell or donate it.
Mobility equipment is transported free of charge by airlines. You could use it all the way from the car into the terminal. She would be able to sit in it while waiting in the check in and security lines. If she can walk thru the scanner, she would do that and the TSA agents would check her wheelchair. If she can't stand, she would get a pat down.
After clearing security, she could use it all the way to the door of the plane, then gate check it. The wheelchair would be waiting for you at the gate when you arrive (don't be in a hurry to get off - it sometimes takes a while to get the wheelchairs brought up and my experience is that the number of strollers gate checked make it difficult to get to the wheelchair. You can still use skycap assistance to have someone help you with pushing the wheelchair even if you have your own wheelchair.
Magical Express has wheelchair accessible buses; request ahead of time for the shortest wait.
There is more information about air travel and ME in the disABILTIES FAQs thread (follow link in my signature or look near the top of this board. The first post in that thread is an index that tells which post has what information).
If you have a wheelchair with, you would not have to worry about getting from the parking lot into the park entrance and could use it around your resort.
Renting from an off-site company.
You would need to work with your airline to see what is available and schedule skycap services. The easiest would be to drop her off at the terminal and then park. You would do the same on the way back. Security would work the same - just that the skycap would push her thru. Gate skycaps would be able to push a wheelchair down the skyway to the door of the plane. When arriving at Orlando, you would do the same thing.
The off-site rental companies will deliver to the resorts. Some companies are 'WDW Featured Providers'. They can delver and pick up from Bell Services without you being present, so the wheelchair would be waiting for you.
There are many good companies that are not 'Featured'; for those, you would need to arrange for them to deliver and pick it up directly with you because they are not allowed to leave it with Bell Services.
Follow the link in my signature to the disABILITIES FAQs thread. Post 2 is about wheelchairs and
ECVs and has contact information for a number of off-site companies.
Park rental wheelchair
The airport would work the same way as if you were doing an off-site rental.
You have posted that her grandson could get one for free, but I don't think the free wheelchair would be worth the difficulty having to go into the park to get one. There are parking lot wheelchairs, but no guarantee that any would be available and you would still have to get her from the handicapped parking spot to where those wheelchairs are.
When you leave, there is no guarantee that a wheelchair would be available to get from the park exit to your car.
And, she would not have one to get around the resort.
I would NOT rent an
ECV for her. It will be very busy during that time period and she is likely going to want to look around at all the decorations. Driving an ECV takes a lot of energy in terms of staying alert and watching for people who might unexpectedly pop out in front of you.