I repaired an old quilt with similar problems. Since this is just a top and not quilted yet it shouldn't be too difficult. More than likely it was made from leftovers of prewashed fabric so I would make sure anything you add is also prewashed. I did exactly what some others are suggesting. I carefully appliqued the new fabric over the old with very tiny stitches. If this were a museum piece, the experts would probably recommend not doing anything at all to it as it can decrease the value of a vintage piece. But since it's something you want to be able to display and handle, maybe even cuddle up with, you want it to be in usable condition. It's so neat to have something like that made by you great grandmother. I love my family pieces, no quilts, but some beautiful crochet pieces and embroidered linens. It's a connection to my past. Enjoy! And do post pics when you're done.