When I had my elderly mother-in-law with me (78), even though she didn't have a disabled badge for the car, I explained to the car park attendant at Epcot that she couldn't walk any distance and they let us park in the disabled area. I could also then drop her off really close to the gates and then park the car in a disabled space. They were really kind and didn't have a problem with this at all.

You can hire a scooter wheelchair for US$30 per day which is great for anyone with mobility problems and also great for those with them as no one has to push the wheelchair!!

If you are going to Universal or Islands of Adventure then make sure that you get the Valet parking. Even the disabled parking at these parks is quite some way from the parks, further than any of the Disney car parks. Valet parking costs US$16 per day, plus a couple of dollars tip, but is so lovely and easy and you are as close to the parks as you can possibly get.