Just a couple quick notes. First, my FIL was in a N/H for many years due to dementia. Often things would disappear from his room - eyeglasses, TV remotes, trinkets - you name it, it probably came up missing at one time or another. I was not quilting at the time but did crochet several blankies for him. These too, would disappear. The missing items were not being taken by staff but by other patients. Every so often the staff would rummage around and find the missing items in another's room or other odd places. I have even seen other patients wearing his eyeglasses! Do put her name on it very clearly, but don't be surprised if a lovely quilt is nabbed by a patient (or staff).
In terms of your MIL, take your feelings toword her out of the picture. Focus on doing this for your DH's GMa. Even if she doesn't have the cognative ability to recognize you, YOU have the ability to recognize her. Focus on your DH's GMa and the love she gave to your DH rather than your MIL - she's a whole 'nother story. Make the quilt how YOU want in the time frame YOU set while remembering the quilt is a gift of love for her not your MIL. Even if she doesn't recognize you she can still recognize love, kindness and beauty.