The problem, Morecy, is that all airline tickets are non-transferable contracts between the customer and the airline. While you may have purchased the ticket, you have absolutely no rights over its use. It's the sole property of the person named on the ticket, and AA is under no obligation to do anything other than letting your mom use the ticket for her own travels within the ticket's validity.
Now, AA may make exceptions on a case-by-case basis for those customers who were traveling on or around the time of 9/11, but many people are milking it and trying to take advantage of the tragedy to get their way with the airlines. While that's not the case in your situation, the airline has to be as consistent as possible with ALL their customers when it comes to their rules and guidelines for ticket usage. That's why you were refused when you asked to use her ticket.
You have every right to feel the way you do, however, I don't think AA has done anything wrong here.
"In this present crisis, government is not the solution to our problem - government IS the problem." - Ronald Reagan
Comments made here are my own and are not intended to represent the official position of Alaska Air Group