I am a little confused. is your intent to have family members color it once and then set the coloring permanently? Or is your intent to create a quilt that can be colored over and over again and washed between coloring in the hopes that all color is removed like those stuffed animals that were quite popular a few years back? Like this:
https://www.amazon.com/ALEX-Toys-Cra.../dp/B000G2HSB6
Then I would think the medium used to color would be just as important as the fabric. For something like this I would use a very good quality bleached muslin and maybe even some nice sharp black and white prints that can be colored in like a coloring book.