UPDATE: I contacted Airbnb and they agreed that the parents were absolutely negligent in this case and they canceled the reservation. So there you have it folks - at the the end of the day, you are responsible for your child's actions. Airbnb also told me that these folks were new to my environment and therefore should have been even more careful given those circumstances.
Because of these careless, and quite honestly reckless parents, I have revised my listing to state no children allowed. It's unfotunate, but sometimes it only takes 1 bad apple such as this to be forced to make that decision.
The mother never apologized, did not offer to repay me for the mirror, she took the position that I was to blame and that she was the victim.