I feel ya! We went with TWO stubborn grandmas who both refused to rent ECV's - "we'll just take breaks" they said. Ha! After a few hours, beet red faces, and lots of pain they both succumbed and rented ECVs. Best idea ever btw!! Now, they rent them every trip. I kinda think they secretly look forward to it?
But, back to your question! It depends? Sometimes they sell out early. You can always rent a wheelchair if it gets to be too much and they are out of ECVs. We went to Disney World in December and grandma waited too long to rent a scooter from a off site company and they were all sold out for our first day. She got one for the second day onward, but that first day we had to rely on DW ECVs, and we headed straight to the ECV rental at Epcot at about noon and everything, every ECV every wheelchair, was rented.
You might want to look into renting an ECV for the duration of her trip. Deckert is a great company that we use everytime, and it's cheaper than the daily ECV rentals at the park. And the scooters are way nicer! They drop it off at your hotel and pick it up too.(714) 542-5607
Good luck!!!!!!