VNC over SSH and you should be set.
You can forward the VNC port with a local port forward e.g ssh -L $yourPort:localhost:$vncPort $grandmasMachine
. Then open Remmina (or KRDC, or some other VNC client).
I do hope your grandma has good upload speeds though.
Bless you for spreading the word of the penguin and being the support of your family. Props to you.