What a great idea! Make sure you take a picture to show us when you are finished.
I would cut the pieces for the cover, then sew the granny square onto the front piece, then sew the cover together. Definitely tack the granny square every 2 inches or so onto the fabric so that it won't some loose. I would use thread matched to the color of the granny square and just take a small stitch up on one side of the yarn, over it and down the other side, about every 2 inches or so all over the whole granny square. I would also stitch around the entire square in a close running stitch or whip stitch to secure the edges.
Don't forget that picture!
Hope this helps.