Dear quilt938,
You and your late mother have received much more than a gold wedding ring and quilt squares. You have something which money or quilt fabric can't buy... memories, love of family, pride, and respect ... even though you write of a dysfunctional family... who's isn't in some ways? Who cares?
If I were you:
* I'd place all the quilt squares in a mesh lingerie bag; gently machine wash and dry; or air dry and lightly press/iron with an ironing cloth to protect the appliques... even ironing from the reverse over a terry towel!
* I'd trim the newer white squares to match up with the older darker ones.
* I'd lay out the squares by alternating the unbleached with the white muslins.
* I'd add a solid colored thin(1"-2") sashing strips between blocks in rows and columns.
* Maybe add a coordinating border, no larger than 4 inches in width.
* Quilt by hand if you prefer. Add a binding.
If its delicate, perhaps don't use it as a utility quilt but as a display quilt and display it proudly for you, your children and their children... telling the "story" and instilling that love and those intangible gifts that you so treasure.
Prayers and blessings.