Well, first, I'm sorry to hear about your stepfather. I hope there's a turn of events for the better.

My wife's grandmother was very ill last year, right before NYE. My wife and I were overseas in Barcelona when we learned her condition had worsened. AA booked us on the next flight out and was even able to get us seats in Business Class for the ride back.

A few months later, my wife's aunt became terminally ill. I called AA about an award seat question, and the agent informed me that they could arrange for bereavement fares (5 of them), domestically to a smaller airport (from IAD to TLH)

So, as others have said, YMMV. But, my experiences have been positive.

FWIW, I was EXP when both of these events occurred. Not sure how much, if any, impact this had.