I just rented a Baby Jogger City Mini Double from Orlando Strollers on our trip last week. Best thing I ever did! We didn't really need the stroller in the airport since there were 4 adults wrangling 2 kids, and we wanted them to walk to get their energy out before the flight. The stroller was waiting at my resort when we arrived, and it was a dream. The seats reclined independently so the girls could nap when they wanted. The sunshades were huge. It folded up with the pull of 2 straps. The basket underneath was a little small, but we had a backpack for all our stuff anyways. Totally worth it!
OP, have you thought about a baby carrier? I have an Ergo and would wear my 20 month old in line if she was sleeping.