It's not a prank. Emma is giving Betty the push she (thinks she) needs after listening to the conversation in the car.
Emma plays the devil part, putting Betty in a tempting situation, so she chooses to stop being a nun.
Emma's initial plan (if on her path) was to sneak into the MC's room once Betty fell asleep. If you accept Betty, she renounces it to give Betty a chance. If you don't accept Betty, she renounces her plan to be supportive of Betty.
I think Emma deserves a prize, not a punishment.
As said above, she deserves a prize, so I think I would add something to your idea. To give her the chance to do the cleaning. Oh, and I would change your "(or literally anyone else in the harem)" for "(AND literally anyone else in the harem except for Daphne and Scarlett in the cleaning part)".