Hi Patricia,
How exciting to be headed back to Disney World. Sounds like your family loves their trips there as much as mine does.
I can understand tired feet. My three boys ages 13, 10 and 8 complain of the same thing during our DIsney World vacations. Information regarding stroller rental can be found
here. I can not recall ever seeing an age or weight limit on the strollers so I went back and checked pictures I took of the rental signs as well as a few of the Disney travel sites. I have not seen any posted information for either.
The Disney strollers are constructed of hard plastic and seem to be pretty indestructible. My 8 and 10 years still occasionally use the strollers and we have pushed both of them, crammed in at the same time, with no problems. The only thing I would tell you is that my boys are on the tall side and no longer fit comfortably in a single stroller. We have used a double stroller a few times and the only way they both fit, is to ride one in front of the other, with their feet sticking out in front of the stroller. While my 13 year old can technically fit in the stroller, it is at a very awkward angle and not comfortable at all. Even with tired feet, he would much rather walk than try to fit into the stroller.
Personally I would bypass the stroller as an option for the 13 year old. Plus for the cost of a double stroller for the day for the 10 year old, you may want to try other options like taking additional breaks throughout the day, or even heading back to the resort for a few hours to swim and regroup.