Ugh...torn on this one.
As a rider, I take care of my stuff. Given the same situation, I wouldn't expect a BO to replace polos that their dog had torn a hole in, especially if I knew the dog was there.
As a dog owner (which I am....proudly), I would probably replace the polos. As a dog owner,I'm responsible for my animals. It's the same for my children. If one of them breaks something, I take responsibility for replacing it. Kids may be kids....but when they break things, they are MY kids. =-) As for the stall door, it's a bit different because she is paying to board with you. It would come down to what your contract states...and while we all think childish things, probably best not to follow through on those thoughts! =-) Then again, if it were my horse and they had done a ton of damage to something at a stable we were boarding at, I would offer to pay. Technically part of the boarding costs are supposed to be for repairs. Everyone pays them and it supposedly goes towards the upkeep of the facility....but anything that I deemed excessive caused by my horse, I would at -least- offer to pay for replacements.
But that's just who I am. Sorry to be on the fence so much with this.
So...I guess my main issue is with the boarder and her insistence in having you replace them. She's shouldn't be....but I can't really control that.