I have a 14 year old that travels alone monthly and this is one of my biggest fears. When he was younger I paid the $150 UM fare and they would never allow him to travel on the last flight of the day. Now that he is older and doesn't want to go the the AA "holding pen" as he calls it I just continue to book him on morning connections. Almost all of his connections are in Miami and my bestfriend lives there so I always have an emergency plan.
All of this being said, it seems like AA could have handled the situation better. regardless of her age, I don't think that anyone should have to wait 3 hours for a solution.