Kids cheat when they're not engaged with the material enough to learn it properly, or when the consequences for not cheating are too much for them to bear.

You gave them an assignment to do when you weren't actually teaching them, which means there's no way they can be properly engaged with the material. And you threatened their spring break with sitting in a room alone doing homework if they didn't get it done fast enough. You created a perfect breeding ground for cheating. Try creating an environment where kids don't feel that they need to cheat.

When I was in university I never heard of anyone cheating, because we were all treated like adults and we were engaging in material we liked. Try inspiring your students and treating them like adults. That means respecting their free time. If you don't give them respect as people, you won't get any respect as an authority.