Getting a
scooter is the way to go. It's cheaper to rent offsite and you'll have use of it at the resort, too. You will be challenged by perhaps waiting longer using Disney transportation; because, you'll have two scooters. Also, you may have to help yourself and get the scooter on and off Disney transportation. This can be a little tough when you are first learning to use a scooter. Getting the scooter in the exact position the driver requires can be hard. If you are using a car you need room for two scooters. The scooters come apart into 4 or 5 pieces. The batteries need to be charged each day. You may have to help getting the scooters in and out of their resort room. Make sure the scooters are off when watching a show, parade or fireworks. You want your battery charge to last the day.
Remember, park tickets aren't cheap and it's well worth the cost of the scooter; so, they can enjoy the parks betters nod longer. They will last much longer with a scooter.
I agree with the previous posters that you need to have a helping hand getting in and out of some of the rides. Some rides can be a challenge with a scooter like Soarin'. You have to use an elevator to get to the ground floor for the ride.
For newbies on scooters it would be good to go to a local zoo and use one there for a day. Practice at the grocery store and other stores where you can use a scooter. Those scooters are harder, but it's good practice and it's free. Yo can practice at the resort, too before heading off to the parks.
Scooters give you handicap access to reserved areas for the parades. You do have to get there early to get a front row seat. I would allow an hour before the time of the parade. For shows you go right to the theater with the scooter. There will be some lines where the scooters will use a different line to get to the ride. There are some rides where there is a moving, walking conveyor like Buzz Lightyear in MK.
Try to mix rides and shows; so, they can have a rest between rides. Eating provides a rest, too. Perhaps concentrate on less rides and do more shows. There is is so much live, street entertainment to enjoy.
If they need a mid day rest for a nap then let them have one. Don't make them overdo.
I think it's a big mistake to think your parents can do this without the use of a scooter or wheelchair. The average guest walks 6 miles a day at Disney World. Between going back and forth from the resorts, the parks, and the ride lines it's a lot of walking. There are some guests that do 12 miles a day at the parks.