I'm going to assume the seat will be rearfacing in the vehicle (no shame in using it ff on the plane, since it takes up so much space) - I'm not gonna be sure on specifics, but you are def looking at a full sized vehicle. Since you have to fit five people, it might be worth it to rent a three row vehicle. Do you have an angle adjuster? Bring it with you for sure or maybe even buy one for the trip. If ff-ing on the plane, don't forget to securely pack the rf boot for use in the vehicle.
Alternatively, to avoid needing to bring along a heavy seat with parts/accessories you'll have to cart around separately, you could but a Cosco Scenera NEXT at walmart for about $50. It is light and compact, will be able to rearface on the plane, and as noted earlier is very inexpensive. You'd also likely have better luck fitting it in the back seat with two adults.
If you haven't bought a seat for baby on the plane and can't get one before you have to leave - I'd buy an inexpensive carseat like the Scenera and checking it in the original box. This will give the seat the most protection from being damaged during handling. Sadly, carseats are not handled with care when checked and can be easily damaged. Even if the seat does not appear damaged, it may have hidden stress damage from being dropped long distances onto concrete or other such mishandling.