I have been nothing but professional and courteous with her, as I enforced the rules of our written lease.On one hand, I think "I'm the professional" and should not dignify her conduct by responding at all, while the other side of me does not want to set a precedent where she can use me as a verbal punching bag during her residency.Another piece of information that might be germane is her unit it totally trashed (she has lived there for 10 years) and would take about $6k to turn it over. 

Then the lawyers would sort it out.What you can do to protect yourself is to: Have clear expectations in the form of a well worded rental agreement; Abide by the landlord-tenant laws for your jurisdiction; Maintain sufficient insurance; Communicate with integrity and honesty; Be polite, courteous, firm, fair, and professional; answer only what is asked of you and do so with fact, not opinion.Unless you were negligent in some way, you should be fine.

You tell both parties that you have spoken to the other party involved and that's as far as it goes...... you have asked them to be courteous to each other about the noise, but you cant force them to do anything.....if the other party is breaking the law in regard to the noise, then call the cops....otherwise, work it out among yourselves....or move out.....DO NOT try to be "mom/dad" and act as the mediator..... its a no win situation

It's 10 seconds out of their life to be courteous and respect other people's time, instead of being rude and selfish. 

He makes enough money, was courteous, clean, dosen't smoke, and was early to our showing.

It wasn't business related but he was a very straight forward guy, easy to talk to, prompt and courteous.

The neighbor one likes the idea and is very courteous about it, but we've had conflicting BBQ nights in the past.

In any case, can we please stay courteous and respectful here?

How professional and courteous do they represent themselves? 

That's part of being a courteous neighbour.