Sponsering a dog is a brilliant idea - I'd never thought of that
. You can also buy lovely childrens' books about dogs, both fiction and non-fiction to help them.
I have to say, as an Adult that learning facts about spiders has greatly reducing my Arachnophobia and the same method got rid of my phobia of Thunderstorms completely, so I would think it's worth a try with your Grandchildren.
Fingers crossed
.