Good Job Henry!!! They are going to love this quilt :D :D :D
Is the fabric that frayed a flannel? Is the other one quilting cotton?
When I use flannel I increase the seam allowance and I also do a zig zag on the edges before putting the binding on. It seams to want to unravel more than quilting cotton. I also wash and dry it twice before cutting it because it seems to shrink pretty good through two washings...