I am a car seat nut and am already planning out what we'll do when we go in February with kids ages 5m, almost 3y, and 5.5y. Although my 5yo will still be harnessed in our cars at home, there's no way I'm going to try lugging her heavy Frontier for the shuttle to/from the airport on our end and one day of rental in FL. I will get her a Bubble Bum and have her practice with it around town for a month or so before we leave. She's already 43" and 43 lbs, so she meets the minimums for the seat. If you would rather a high back booster, you can get something like the Graco Turbobooster, pack the back in a well padded suitcase, and have him carry the lower part on as a carry on, stored in the overhead compartments. The baby will have his baseless infant seat. Still debating what harnessed seat to bring for my middle, who will turn 3 a few days after we get home. He is average height but only 23 lbs still at 2y4m. I may pick up an inexpensive lightweight harnessed seat for traveling with him. He will still be rear facing at home and likely in the rental car, but will forward face in his seat on the plane. The Ride Safer vest is also a consideration, if I'm willing to spend the money and forward face him in the rental. If he were already forward facing full time and we were planning to have a car for our entire trip, that is the route I would probably go.
You really want to avoid renting car seats, as you have no way of knowing what the company will provide you with, whether it is expired, suitable for your child, has been in any kind of crash (for most seats, even a fender bender counts), is filthy, etc. Also avoid checking your seats with luggage; they will certainly be quite abused, which may cause damage, seen or unseen, that could cause them to fail in a crash. You also run the risk of the seats not making it to your destination - lost luggage. If you can't use them on the plane, gate checking is the safest option.
As far as transporting them in the airport, consider a luggage cart and bungee cords. My Target has luggage carts for around $15 in the luggage section. Kids can ride on them that way as well, which will be nice for us as we aren't flying with a stroller.