My aunts usually use carseats in the plane, and they usually have relatives pick them so they need that carseat for the private vehicle.
My 2 year old would rather sit just like everyone else instead of using the carseat but I usually bring it along... you can pick up the car seat baggage cart at Babies R Us, you just strap the carseat onto it and can haul it around. I believe your 2 year old can even sit in it while you are hauling it around so you don't have to carry her when she is tired.
A lot of shuttles are like small buses, the seats are all different ways/positions and most don't have seat belts. Some passenger vans have seat belts and some don't, it all depends on if the company has taken them out... or if the seat belts have been jammed into the seat.
If you decide to rent a car most places provide a carseat, you just have to ask. I think that is a great and a huge lifesaver.
Best wishes on your travel!