It isn't about singing, but "Hula Girls" is a charming recent Japanese movie that made it into US release. It's about a reluctant dance teacher from the big city going to a remote mining town to teach hula dancing. I think it would apply to the model you're looking for.
Of course, the script is in Japanese. But if you watch the movie, you'll see that the in-studio teaching scenes are not simply teaching scenes, but integral parts of the overall story and character development. The teaching parts, while adding interest and color, are just plot devices, which is as they should be. I suppose you need just as many teaching scenes as are necessary for the story development, no more and no less. The instruction scenes must be part the story on more than one level, not something thrown in on top.