Sorry to hear about your loss.

My experience with BA was less flexible than others have reported when my mum died - I wonder whether it's the agent you get to speak to that influences what they will and won't do. Even with the death certificate, as my mum wasn't on the booking, they recommended that I go to my travel insurer first and then come back to BA if the insurer wouldn't do anything. It wasn't a good experience for me - even though I was a GGL back then as well. Luckily my insurer (through NatWest Black) was exceptionally helpful.

I hope that you have a better experience with AA - I know that their change policies and allowance to use the fare balance is generally more flexible than BA.