Sorry for what is happening to you and your family.

I had a similar situation three years ago and we call AA and find tickets for the same day at special rate, we did not ask but the operator knew that something was wrong because I was crying and all that so then she asked me about the reason of the "last minute trip" and very polite told me about this special rate, however they will ask you the name of the funeral home or the hospital were your relative will be, just to be sure is for real... I guess.

We got 50% off the regular price on that day.

Sorry to hear about your grandmother-we were in a similar situation this past August, anticipated but happened more suddenly than expected. Ticket prices were expensive when I looked on-line to book our son home for his grandfather's funeral so I called the airlines directly-Midwest could not get us a ticket for three days and the price was still expensive but cheaper than the listed price. NW got him on a flight that got him home 12 hours after his grandfather died-it was so quick he wasn't sure he could get to the airport in time having to drive 1 1/2 hours to the airport and the phone call taking place 3 hours after the death! and they upgraded him to first class when he got to the airport. We needed to give name of the deceased and funeral home name but to our knowledge nothing was ever checked up on. The best part was the return date was flexible with no penalties and we did have to change the date that we originally gave because the funeral arrangements were not able to be made as quickly as hoped(we had to get our son back to school so were on a time frame)and we did not incur any extra charges. The ticket price was about 1 1/2 times what we normally pay but less than 1/2 the listed price at the time. One airline extremely helpful in a time of need and the other was unbelievably rude. So keep trying if not successfully initially and blessings to you and your family!!