Our dog (pitbull) was on a walk and on a leash, daschund was in it's yard and acting aggressively, but there is a decorative hole in the wall. Daschund stuck nose out of hole and pitbull bit off daschund's upper jaw in one swift movement. Police were involved and said that since our dog was on a leash we would not be held liable. This could have been avoided if the hole in the wall had been screened off, as many neighbors in the neighborhood do. Owner of daschund is threatening to sue if we do not pay them $9,002 in vet bills. This was after they wrote a letter with our address on it to every single neighbor about how we own a vicious dog (he is not vicious, but was seemingly protecting my sister who was walking him from what he though was a threat - dogs cannot discern size)
Trademark Application Attorney
As I said in response to your other question: Anyone can sue anybody for anything - whether or not the suit would be successful is impossible to predict. However, to play devil's advocate for a moment, I can see how you might be held at least partially responsible - although your dog was on a leash, your sister knew the other dog was acting aggressively and yet she did not move your dog away. If she is too young to make that determination, then she is too young to have been walking your dog.
Given how this has turned so ugly so quickly, I suggest you speak with a local attorney for guidance. The State Bar of Arizona can give you a referral: www.azbar.org/ You may also need to notify your homeowners insurance carrier.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.