Stuck because of American airlines

My sister flew here for Christmas from NY.Her husband is in the army and all the could manage was 8 days free time so they needed airline tickets.I found American airline tickets for a few dollars cheaper then other airlines so I told her to get them but she said she has never used them because so many people have told her horror stories about delayed flights,rude people that work for the airlines and about being CHEATED out of money.I told her that she should fly with them,because not every flight with them could be bad,right?
 Well,I was WRONG!My sister took my bad advice and got those tickets which really only ended up saving about 20 bucks.(My sis is a very experienced air traveler and she is used to all kinds of travel and she has never had anything like this ever happen even with long international flights).
 Of course bad weather was going on up north but that did not cause any trouble for my sisters flights because they were ahead of the storm but still they had delays because of Christmas travel. So,on the way here my sister and her family did have to spend the night in an airport which was terrible and unexpected but she did not complain about that,nope.What is going on that is terrible and even worse is that my sister arrived at 6 am to MEM. and was waiting to fly at 7.30.She got on that plane when all of the sudden people start to wash the plane and do oil checks while the travelers were on the plain ready to fly.The workers were behind schedule.When my sister made it to Chicago her plane from Chicago already left with out her!!!This was the air lines fault but they were not apologetic nor were they helpful at all.They even told my sister that it may be a few days before they had any flights for them!!!!My sister asked if they would pay for a rental car and they said maybe she would get a little money back from them but maybe not ,they weren't sure if she would get anything.The rental car was over 400 bucks and would take 12 hours of driving in yucky weather to get back.So right now,she has no clue what top do and not much money. She may be stuck at the Chicago airport with her hubby and 3 year old daughter for days or she may have to come out of 400 bucks {which she does not have to spend}and just be out of more money!!
 I feel so terrible!!Have you had a bad airline experience?? Have you ever flown American?? Please let me know.