I have a couple of kids... hope this helps.
Carseats on airplanes suck, however, they could potentially save a child from danger in a rare case of severe turbulence or even rarer accident.
Carseats are also good as straightjackets for kids, without all those annoying hassles with the child protection agencies. Kids love airplanes. They make great jungle gyms, much to the dismay of the other folks in the cabin. I fly my kids a lot, and it doesnt make any difference. Airplanes = playground. Carseats provide a place to easily go to sleep.
I have gotten a bit lazy i guess ... I hate dragging two carseats around, I used to do it with just one kid, but having multiple children, a wife that weights about as much as the car seat itself, etc. i am just checking them and putting the 2 year old directly into the seat.
During take offs and landings, i usually hold her, but i have that seat for them to sit there on a general basis.
What you could do is get a small booster (without back). The difficulty with the bulkhead in particular is nearly every car seat designed for a 2 year old's weight/height/etc will not fit. If you can get one to fit, its likely too small for the child. Otherwise, yes, you could just raise the armrest. You could probably fit a britax with ease in a first class seat. (yes, i fly my kids in first class whenever technically possible)
There is ONE carseat that i would recommend. Its sort of a stroller/carseat/airplane seat all in one combo. It weighs a ton, but it will fit in the aircraft.
(sarcasm) And if you do not want to deal with the kids, you can also upgrade you and the SO to first class, and let the flight attendants take care of them. You dont even need to pay the unaccompanied minor fee because you are technically someone they know sitting on the airplane. Thats the FA's job right? I would never, ever, ever do this...but you would not believe some of these gate agents!!! I had a couple of them try to arrange this for me!! I really suspect they hate some of the flight crews and try to give them heck. Maybe they were non-union?
For a lot of info on this, read some threads or ask questions in the kid/family/etc travel forum on flyertalk. I found them useful:
http://www.flyertalk.com/forum/travel-children-221/