Rental car seats aren't a good idea at all.
There is no way to know if the car seat was in a crash (and no way for the rental agency to guarantee that unless they only rent brand new seats each time) and most reports I've heard revolve around the seat being outdated/incorrect type for their child/lacking instructions/dirty..etc, etc.
Best option is to just use the car seat on the airplane and then use it for the time you need to at your vacation destination.