When my Mom was in care, I made her a lap quilt with ties, and it worked great to attach to the metal side supports. All I did was use pieces similar to a shoelace, and fold them in half and stitch to the top corners, right through the quilt. Her care home had no problem with this, but "if" your Mom is in a care facility you might like to check into that first.
To make it so your Mom can tie it around her waist, you could bind the 3 edges as normal, but then make like an apron band with attached ties for the top edge. The only problem I can think about that is, the bow might dig into her back while sitting?