Have you asked them how interested they are in having a part of this quilt?
I know in my family there would be some who really wouldn't care at all about getting it, others who would want it all to stay in one piece and one who might truly treasure the section that was "theirs".
I know, not much help, but I would probably want to keep it all in one piece unless somebody really, really, really wanted the part pertaining to their family.