You're right to be worried. Lap babies are not safe, and are not recommended by the FAA, AAP, NTSB, and technicians. They're a danger to others as they are projectiles. Or they'll be your airbag. It's also just simply harder to share your three cubic inches with someone else who doesn't understand, "the seatbelt light is on and you need to sit still now."
It's also not safe to check carseats. They'd be considered crashed, as they're generally thrown around many times between when they leave your arms and when they arrive back (if they're not lost in the process, just like any other luggage). They're a lifesaving device. You put your kids in them to potentially save their lives. Are you just going to trust every single person between the ticket counter and the baggage claim to treat them like you'd treat them?
[ame="http://www.youtube.com/watch?v=lzmJr1a-BHU&feature=player_embedded"]Mistreating luggage - YouTube[/ame]
See the pile of carseats to the left?
I'd call the airline back and book another ticket.
Rental seats are not known for being clean, well cared for, not expired, not recalls, and who knows who has eaten/peed/pooped/puked in them, and if so, how were they cleaned. We rented a seat on one trip (actually two seats since it was a two legged trip) and when we got there with 10 WEEK old Piper they brought out a booster seat. I sent it back, and after many many minutes they found me an infant seat without a base with no instructions, no stickers, no DOM, no nothing. To this day I have no idea what it was. On our second leg they gave me an infant seat with a base and some stickers. Much better, but still not good. We never traveled without a seat of our own again.
I'd probably get two BubbleBums or Lite Riders for the older two kids to travel with. Take them on board and put them in the overhead. Then I'd put the two year old in the Radian forward facing on the plane, but rear facing at the other end. Bring the rear facing foot separately. Then I'd bring the baby's infant seat. That way you don't need any top tethers at the other end, so no need to worry.
The two year old and baby will go next to the windows (if it's a 3/3 configuration I'd just book six straight across if you can), then either a parent or an older child, then the other person on the aisle.
Let us know what strollers/luggage you're taking and we can help you figure out how to get the seats through the airport. Probably the easiest thing to do is to get backpack straps for the Radian and wear it, and put the baby in the Snugride in a snap n go or stroller. Have the older kids carry their boosters, or put them in the stroller's basket, or if you get BubbleBums, in a carry on bag.
Wendy