When we flew to Montana when the girls were 10 mo and 2yrs. they each had their own seat on the plane...back then, Delta offered 1/2 price for kids 3 and under IN A SEAT!!....anyway...the flight attendants allowed me to go on board early- and buckle in their seats in the proper seat....of course, after 9/11 I doubt they would let you on early... This worked great for us..
When DD1 was 5, we went to Houston for a long weekend just before xmas- (cousin cancelled her wedding 36 hours prior to our flight- non refundable etc.. blah blah....)..anyway- DD2 did not go,she stayed home with DH....DD1's car seat was shipped with our luggage...they bagged it, similar to what they do with strollers.
I personally, would NEVER use a car seat that was not mine...how do you know if it's been in an accident?? you dont...you dont know if it's on the recall list- since by the time you know what your getting, it's already time to take the car to disney

Basically- my thought, is you should come up with a way to get your own seat there...if your kids are use to sitting in a car seat, they wont mind doing it on a plane..
Now- if they are in a high back booster seat- you CAN NOT use these on an airplane...they are not designed to be used with the single lap belt ---this is why DD1's had to be checked for Houston, she would have preferred to have it- since it's easier to see out the window..
Oi- this is longer than I had planned- sorry
Brandy