What airport transfer do you have booked? Most of the private car services/ limo companies I've worked with will provide a car seat, but I haven't done it in FLL so maybe it's different there. I'd be surprised if Uber provides car seats unless that driver happens to have one anyway, since Uber is people using their private cars. I've seen recommendations on the boards for "Bubblebum" which is an inflatable booster seat, if the kids are old enough to use a booster. Would it be possible to bring the kids car seats on the flight? Many little ones are more comfortable in their regular car seat than on a lap or airplane seat. You can also check a car seat without fee or having it count towards your baggage allowance, though I'd be concerned with possible damage. I have heard of renting car seats from BabiesRUs, though I've never looked into it.
Enjoy your cruise!