I'm wondering, legal gurus... would the other child's parents have a case against OP for lack of supervision?
Only the owner's daughter was injured. The other child was not so there is no reason for the parents of that child to look to the owner for anything. The other car owner could have a negligent entrustment claim against stayn100.
I was told the friend would be in trouble for the stealing
No, the friend didn't steal anything. The friend had permission to drive, give by the person who had possession of the car.
If anybody stole anything it was your daughter. If you want to report it as a theft, she will bear the brunt of criminal charges in addition to her injuries. Do you want that?
And, frankly, I think your daughter had constructive permission since the keys and the car were available. That puts you on the hook for negligent entrustment with regard to the damage to the other vehicle.
As for the damage to your car and your daughter's injuries, the other child is indeed responsible for her own negligence. Good luck getting any money out of her or her family.
And where do you come off bringing any car home without making damned sure you had insurance. Notice that there is no question mark at the end of that sentence because there is no excuse. You're your own worst enemy. This debacle is going to cost you big time.