I like QuiltingNinaSue's suggestion.
You could also take several photos of GM's quilt, including good clear close-ups, and put them in a collage frame to be hung near where you might use a new reproduction of her quilt, made by you.
I think of textiles as living things; and therefore they generally have a life span. We can treat them as healthily as possible, but if we love them and spend time with them, eventually they grow very old and leave us with memories. In my opinion, creative ways of keep the memories fresh is sometimes more practical (and, yes, even loving) than hanging on forever to the tattered and very worn textile as a way to remember the person/place/event for which it was made.
My own family quilt, made ca. 1780 or earlier, was so badly damaged and loved when I received it (passed down to me as the 5th generation) that it couldn't even be shown or used at all. I had to make the hard decision to give it to the Textile Museum at Colonial Williamsburg for research and safe keeping for future studies. Even they do not show it; it lives in the 'stacks' in a humidity, light, and temperature-controlled environment. Someday I will remake this quilt. Someday.