I agree that it's theirs to do with as they want. How they decide to use it is between them. However, if I was asked to make another one, I'd either decline (my choice) or make a very simple quilt for them and not worry about it. Sadly, your Goddaughter really doesn't appreciate the work you put in the quilt and chooses to treat it like a Walmart quilt. Makes me wonder, if this is how she treats something she loves, I wonder what she'd do if she didn't like it?
BTW, I have 4 dogs, two of which sleep on the bed. I've always had multiple dogs and I've never allowed them to ruin comforters or quilts.