If you will be driving much at the other end, I'd definitely bring your own seats, because you can use them on the plane (which is what FAA and NTSB strongly recommend anyway). Get either a Traveling Toddler or a cart and just strap the seats to that. The caution with rental seats is that their histories are not known--in addition to not knowing how other renters have treated them, you don't know how the car rental place treats them (and occasionally places have tried to rent expired seats because they don't know to pay attention to that, so double check that). If you are just driving a few miles at the other end, I'd probably worry less about it.
Alternatively, split the difference and just bring the Nautilus; use it for your three-year-old on the plane and get a CARES harness (good for children up to 44 lbs) for your five-year-old. Assume if you rent one seat it should be relatively easy to get one that fits your three-year-old, and you'll know you have the Nautilus for your five-year-old.
You can also consider getting a lighter travel seat if your budget allows; the SureRide weighs half of what the Roundabout weighs and is often under $100. If you are looking at renting a seat for any amount of time, you might make up the difference to that (or to the even cheaper/lighter Scenera, though it's also smaller so your boys might be close to outgrowing it) pretty quickly.
Finally--are you going for vacation, or to visit family? If the latter, you might also look into having a cheaper seat shipped directly there and having them meet you with it at the airport. Then it can live there if there are other children who would use it, or you can bring it home with you and at least be saved taking it one direction.