How old is your grandson? Disney rentals are very expensive and really won't accomodate an infant.
I vote for bringing your own. It's really NOT hard to take a stroller on an airplane. It's actually my vote for our family (3 kids) to bring 2 strollers, because even tho the 4 year old won't use a stroller in the airport, we can pile up our carry-on bags on it to make the walk to the gate much easier. You just get it tagged at your gate, collapse it, and leave it right outside the plane door, then pick it up right outside the plane at your destination.
If this is for an older child and you don't actually have a stroller at home for him anymore, it's still cheaper to buy one (check weight limits) or get one off of Craigslist/yardsale than to rent one. If you buy a new one, you can resell it when you get back as having a week's worth of use and make almost all of your money back.