Another yes vote, for the same reasons as TracyM mentioned. Plus you won't have to wait in the stroller rental lines and I'm sure your's is much more comfortable than theirs (not to mention the additional cost if you rent from the parks). If you buy stuff you'll have to lug it around with your children as well to the bus, car, monorail or boat. After walking a long day you're not going to want to do that. We always bring our own.