I agree with the other posters.
It is possible get a wheelchair from the resorts, but even Disney says on their website that if you need one, you should rent from one of the off-site companies.
So, if having one at the resorts is not vital for your granny, it will probably work out OK to get one from the resort. But, if she will need one both at the resort and the parks, I would not take the chance.
If you do, I would suggest taking the phone numbers of multiple off site companies with you. Better to have them in case you need them.