It seems like a fairly honest mistake to make... I don't have kids but I can reverse the scenario. If one of my parents were alcoholic or addicted and I saw one of their good friends getting help, using them as an example would probably be my first thought too.
I would think it would only take a very quick "hey I know you mean well but I'm really new to sobriety and don't feel comfortable with you discussing it with Jess or anyone else" would probably snap her out of seeing you as an extension of her daughter and make her realize that she's crossed a line. Calling it out in front of the group sounds like an aggressive first step to make.