Allow me to express my condolences as well.
When my father passed away last year after a four year battle with cancer I was fortunate enough to be visiting at the hospital, and I had to delay my return flights home scheduled for that evening for a week or so. I had also already booked my next visit for two weeks later on a different airline and cancelled those entirely.
The first airline, American, changed my flights very readily and gave me an address to send a copy of the death certificate to for a refund of the change fees and fare difference. I'm not sure how long it took to process the refund, but it wasn't a full credit card billing cycle.
Delta, the airline for the second flights (which were cancelled entirely), just asked for the name of the funeral home, noted that in the reservation, and refunded to "airline credit" the entire cost of the tickets, with no change fees ever involved.
I thought both handled it well, although it was very nice to not have one more place to send a copy of the death certificate in Delta's case.
Spend time with your family while you can.