NTA I don't think you were out of line. She was lying, paying others to do her work, and plagiarizing for how long before the teacher found out? That's not a normal 'go to your room' situation and needed some higher form of punishment and since the trip was that close, I think it was warranted; harsh as it may be. She has to get it thru her head that what she is doing is NOT ok and she's not entitled to trips to Paris for cheating.

I do think you need to find out what is causing this though. There has to be something more than just laziness. I remember when I was a kid, I forget what age, but I was struggling in school. I had no interest in reading, wasn't doing the work. I just wasn't focusing right or interested in any of it. I had to get into some different kinds of classes but it helped. Either she is bored based on the level of her classes or she's struggling with something. Maybe have her see a therapist or something. good luck.