Also, the carseat rental company here (from a baby rental supply place) AND the rental seats at one of the car rental places (I forget which) both told me they "thoroughly clean the seats after each use" as per some law regarding shared baby equipment (same one that requires day cares to clean things...). I asked HOW they clean the seats.
"We spray them with a bleach solution, and if there is vomit/food on them, we wash them in the washing machine" Yes including the harness.
I looked at their seats and they looked PERFECT, clean, not expired, not damaged. BUT the straps had been sprayed with bleach and/or chucked in the wash. So not safe at all.
In your situation I would:
If possible have someone help you when you first get to the airport, they can bring your check-in baggage up to the check-in desk for you, so you dont have to worry about handling that (if you cant do this, the airline people will help you, you can get a bellhop guy to take your bags, or you can rent a cart to carry them)
Bring a double stroller, put the 2 carseats in it - snap the infant seat in and strap a convertible on top of it. Older child rides in the stroller, baby you wear in a carrier. Diaper bag you put in the stroller basket.
Once you get to the plane, older child walks, you wear the baby and carry the convertible/diaper bag (someone will offer to help, they always do!). Use the convertible on the plane.
OR
Buy 2 small luggage carts (I got mine for $12 at walmart) and buy one more convertable for the baby. Strap each seat to a cart, strap each kid in a seat. Get a back pack or other easy to carry diaper bag. Then pull one kid/carseat combo with each hand. I've done this but with one kid/carseat, one rolly bag, one backpack full of stuff, and one small suitcase with wheels full of ds's stuff, plus food. Its totally doable.
OR
You said if their seats arent any good you would run out and buy some - who would watch the kids at the airport while you go buy some? If someone is meeting you at the airport, you could have them buy/bring a seat for the baby, and you bring just a convertible for the 3yr old
OR
RSTV for the 3yr old, and bring a convertible for on the plane. 3yr old in the convertible on the plane, and then in the car baby in the convertible, 3yr old in the RSTV. This only works if your 3yr old is big enough for the RSTV.
I would cancel the trip and not go at all before I'd resort to using a rental carseat. Its the same as buying a used carseat off craigslist, you never know what happened to it before you put your own kids in it, and for me, its not worth the risk. It is possible to travel with 2 kids and 2 seats, and yes its kind of a pain in the butt, but at least you know they will be safe!
OR