A carseat is not allowed in the row immediately behind the exit row. The passengers should have been reseated before takeoff. Once reseated, she had every right to install the car seat rear facing. The FA's fault here for not ensuring compliance with the rules.

I too have been in similar situations before takeoff, and simply refuse to take my seat until appropriate ground personnel board the plane and resolve the issue (typically to my satisfaction when equipped with the airline and FAA's regs as in this case).

Unfortunately, once in the air the pax has no power in the situation and if they disobey the FA's orders is likely to be met by law enforcement upon landing. Hope AA makes it up to her.