Yes, the non-compete agreement really only holds water if you can prove that you are able to offer the employee full-time work (meaning 40-hours or more a week) And I really don't know of a dance teacher who would work 40 hours per week without going postal at some point. You'd burn out the employee with that class load.

Non-compete is really a good faith moral obligation and ethical choice, not so much a legality.

Sad, but true! The other side of the coin is to build your school around great teachers (notics that's plural!) not just all of your eggs in one basket with 1 great teacher. This will decrease temptation for students to leave if one teacher walks.