for privacy to be violated there needs to be the expectation that privacy exists, an otherwise non-public individual has a right to privacy from: a) intrusion on one's solitude or into one's private affairs; b) public disclosure of embarrassing private information; c) publicity which puts him/her in a false light to the public; d) appropriation of one's name or picture for personal or commercial advantage.
invasion of privacy is the intrusion into the personal life of another, without just cause, which can give the person whose privacy has been invaded a right to bring a lawsuit for damages against the person or entity that intruded. it encompasses workplace monitoring, internet privacy, data collection, and other means of disseminating private information.
"the supreme court has ruled that there is a limited constitutional right of privacy based on a number of provisions in the bill of rights and subsequent amendments. this includes a right to privacy from government surveillance into an area where a person has a "reasonable expectation of privacy" and also in matters relating to marriage, procreation, contraception, family relationships, child rearing and education." https://www.privacyrights.org/more-privacy-topics
so, your workplace actions, while working, used as "case scenarios".......performed in public (where there is not the expectation of "privacy") may not be protected by federal law but may be protected by state law. if she uses the "situation" and asked "what would you do" and excludes disciplinary details (which is personal) she's probably in the clear legally, no morally and professionally is another story. i am not a lawyer but as a manager you are (or should be) pretty well versed in employment law and privacy laws.......if you want to be a good boss that is......
i agree that your boss has bad manners and shows professionalism and is clueless in her behavior. i am pretty sure she probably isn't mature enough to understand that what she is doing is bad form but you should have a conversation with her just to make your position clear and specifically if she want to use stories about the office she need to leave your name out of the conversation. if you don't get anywhere you can always go to the next level and tell her boss to put a lid on her mouth. but this is may very well be a real personality flaw on her part and you may need to make a decision on whether to work for her or not.
i have found once a gossip, always a gossip.....the question is do you want to work for one?
good luck! :d