First with restrictions?
 

On aa. com, I can choose "first with restrictions" to get a first class seat at a reasonable price. I am trying to get my elderly mother from Connecticut (BDL or any NY area airport) to Arizona. I just checked DL and CO, who fly nonstop between the east coast and PHX, and did not see any similar F option. Am I missing something, or does it not exist?

Most airlines have it. For instance, on DL you'd need to click on "refundable" to make sure you don't possibly get restrictions. It just may appear differently on different airlines. The only one that I know of that doesn't is AS, which has an F fare similar to the "instant upgrade"-type fares of other airlines.