Sounds like you have a plan for this well loved quilt. Just wanted to add that if you choose to use Minky for the backing I think all of you will be happy with it. In my experience it washes and dries without any problems, plus I don't think it will ever pill. I use it for grandkids quilts routinely. They love the feel of it.

I think what I would do is some applique over the hole like a pretty butterfly

I think I would repair the hole with appliqué as you planned, Minky over the fleece without removing the binding. just turn edges under. Do minimal quilting to hold the new backing. As a grandmother myself I have repaired until repairs were all that was left. Once they start coming apart it never stops. Start a new one now and she will love it just as much.

Thank you, everyone, for your kind and helpful comments. I ordered Minky for the back and I will just put it over the existing fleece. I will zig zag over the seams and this will hold the backing. Also, some heart appliques, one over the hole and others to match.

I really appreciate your comments, jokir44. I have been chastising myself over poor workmanship but your post made me feel better about this. When I think of all of the quilts that I have gifted, I would hate to think that they are all falling apart. Thanks again. I so appreciate everyone's help with this project.

This is my opinion, too. I'd put an applique over the hole so it doesn't get larger and leave it as is. You are going to put a lot of time and effort into reconstruction that you could be making a new quilt. This one shows the love/use and abuse given to it when your GGD was a little person and will be a treasure in years to come--even the markers!

I agree with bearisgray, fix the holes, let her love on it some more and make her a new "big girl" quilt. Fixing this one will be a lot of work and she will probably outgrow it in a few years. Her first quilt from you can be washed and put away for for those trips down memory lane.

It's not poor workmanship. Your GGD obviously loves this quilt and has it near her no matter how adventurous she is feeling.
It's a beautiful quilt.

Put this one up and make a 'big girl" quilt. 20 years from now, it will recall great memories.

I wouldn't even bother with the holes! just make a new one and let the old one die, while being loved to death!

I recently repaired a quilt my sister made me, because the back was completely disintegrating (the back was made with an old blanket). My quilt though was not quilted, only tied, so it wasn't too much work to take it apart. I took it apart and replaced the back with cotton fabric, replaced the binding, and retied the quilt (while also adding more ties). Anyway, I would definitely replace the back with something that's maybe a little more durable. And I like your idea with the appliques. It's a really beautiful quilt.