Usually I take the passenger's side on these issues but not here.

Simply put, Mom should not have booked a non-refundable ticket so close to the delivery date. We all know that babies arrive early/late, sometimes with complications. If it was important enough for her to be with her daughter, she would not have tried to cut it so close. Or she could have booked Southwest, where her maximum risk would be a required upgrade to the $299 one-way max.

I have found AA to be very accomodating when it comes to real emergencies. My friend (no status) just got a $290 bereavement fare from AA (midweek travel) when the best the others would offer was $1000+.