I recently played the very short visual novel game Grace's Diary (play it here, more info here). It looks and feels a bit like Hotel Dusk, except it was made for a contest to educate players about teen violence without using violence in the game. You're a teenager concerned about your friend, and you look around your room to remember things about your friend that will convince her that she's actually in an abusive relationship. For some reason when main character is remembering these things that made her uncomfortable it feels natural and not like "here are the signs of an abusive boyfriend!" It's also somewhat difficult to get your friend to leave her abuser.
Seeing how natural it felt to have relationship education in a visual novel made me wonder what other types of knowledge visual novels might be well-suited to teach. With their emphasis on dialog (and choices), I think it would be fairly easy to make educational games about other types of relationships--like how to interact with screaming children, how to assert yourself in a conflict, and how to make a polite request. Of course, writing that type of game assumes you know what the best thing to say is, which can vary a lot depending on the situation.
N.B. It looks like the same developer, Hima, made another really similar game another year for the contest called Janie's Sketchbook. This time the protagonist had some bad relationship habits!