Just visited with my G'ma and aunt who both have limited mobility.
Rented ECV's at Epcot for the day for both of them. My aunt frequently uses them at the grocery stores and is a pro. However, last year her battery ran out about 100 yds. from the rental counter and we had to exchange. Guess what happened this week? YUP! Battery ran out in the middle of the ramp up to the Land Pavilion and we had to wait 20 minutes for a replacement!! (And the CM was kind of rude about it. She actually suggested to me that my aunt wasn't using it right. Uhhh...she was just driving it? How else are you supposed to use it?)
Long story short, make sure you get a CHARGED one before you leave the rental area.
They really are worth having and make those that have limited mobility enjoy the park just as much as those of us with full mobility.
Also, at Epcot, HC parking is located at the front of the parking lot but, the parking field is loooooong. There is a station at the end of the row with courtesy wheelchairs but don't count on it to be stocked. My fam didn't need them but it could be an added inconvenience to those that are dependent on some sort of assistance.
We also discovered it's easier (faster) to drive to the park and park than wait for the dang bus. I have an annual pass though so we parked for free and we had our handicap hang tag with us for the car.