That is a wonderful keepsake. Not sure what size it is, but looks like a nice size lap or larger quilt. If possible I would keep it as original as possible & maybe just put a sm. bias type binding (like 1/2" or 1" folded bias tape) around it as it is. Let it stay "wonky".
Will be anxious to see how you choose to finish it w/pics of this treasure.
Happy quilting