Hi, Victoria!
Any of the rentals (wheelchairs/ECVs/strollers) are available on a first come, first served basis and when they are all rented, that is it. They are rented and returned all day long, so the supply keeps getting replenished throughout the day.
The good news is that you only pay for the rental once a day, so if you change parks, you can get another one without charge (based on availability). Just keep your receipt.
If you are worried about not having a wheelchair for your mom, you might want to consider renting one from an outside company. By doing this, you will not only have the wheelchair for the parks, but also for around your resort, Downtown Disney, or wherever you venture to!
Read the information from the website on rentals and outside companies. Hopefully this will help you decide how best to secure a wheelchair for you mom during your magical Walt Disney World vacation!