M.
Yes, I have gate checked my double stroller on several occasions.
You will be happy to have it - the problem with renting is that you have to give the stroller back at the gate and you could be stuck carrying three tired kids to the bus or car and into the hotel. I would actually take an umbrella stroller for the oldest - there were several nights we carried the smallest out because the two oldest were exhausted (but happy!) and taking up the two stroller seats. You could check the single if you don't want to gate check it, but it will save you a lot of carrying!