I'm sorry you feel the way you do, but you gave them the quilt to use and they have done just that. It's been in use for a year and a half, not hidden in a closet, not hung on the wall, but used on their bed...of course it's going to feel "worn".
If you feel it's still worthy of entering in a show, then it can't be even close to being in the 'abused' category. So show it, if that's what you want, and then when you return it to them afterwards, thank them very much for letting you borrow their quilt for the month or so you had it and tell them you're glad they enjoy it so much. Period.
There is absolutely nothing that is worth the risk of driving a wedge between you and your children. Not one single thing.