Well not my style (I abhor making her smile, I want to hear her screaming), but ig conventional torture is the answer?
Maybe you're worried about leaving marks or damaging her dancing capabilities. Electricity isn't my favorite brand of torture but it might suffice. That or simple slappings, pink belly and spankings are dank.
False hope is another nifty thing. Or carrot and a stick.
What kind of girl or what kind of torture you can use to make her smile ?
Torture is not gonna improve her signing or dancing.
But in that situation I woud use some relatively mild torture methods that leave no damage and no long lasting pain.
So I woud will her with enema and make her wear butt plug.
I woud putt catheter in her pee hole and not let her pee until she finishes her lesson.
I woud stick needles in her breasts as punishment for making mistakes.
also I woud make her perform naked with her student name tag attached to her nipple and also make her wear high heel shoes.
when she is dancing and if she makes A mistake I may throw a dart at her