Hello, I'm Dr. Deb and will do my best to help you today.
This is obviously a really tough situation for all of you.
There may be no obvious "right" answer in this type of situation but if faced with it myself, I wouldn't leave her in your grandfather's house if she's going to be alone there with only someone to come in and feed her during the day. I think she'd be much better off with you even though cats typically don't like change very much.
If left alone, I'd worry that she might harm herself or become ill which might go undetected for a length of time.
If you do decide to take her with you, then I'd suggest use of Feliway which is a natural pheromone designed to reduce stress and anxiety.
It comes in a spray or wipe (for the carrier, just be sure that it drys before placing her in it) and a defuser which can be plugged into the wall at her new home.
If she likes oral treats (such as Pounce), then use of Composure Chews may be something to consider. They're basically the oral equivalent of Feliway.
I just think she'd be happier with you than living alone; she's going to miss your grandfather either way but at least she'll have you who she knows and loves.
I hope this helps. Deb