I wonder if it would be acceptable to get a nice wide backing fabric and tack the yo-yo's to that.
I would consider it a family heirloom - starting with you Mom. If it were mind I would tack it to a plain white backing fabric which would avoid the "back of the fabric peeking through" look and if you wanted to create a label with it's history.
Left along with just added stitches here and there would keep it too fragile for future handling, in my opinion.
Now I know what to do with all the "travel project" yo-yo's I'm accumulating! ;) Thanks for sharing the pics.