Employment authorisation comes with L-2 status, so no separate sponsor is needed. Teaching, however, is licensed by the state, and an Ontario teaching certificate is not automatically recognised. The certification process runs on its own timetable and should be started as soon as the destination is known.
Federal permission, state qualification
Two separate systems govern whether a spouse can actually take the job she wants. The federal one is straightforward: a spouse admitted in L-2 status is employment-authorised incident to that status, may work for any employer and is not tied to a particular position. The state one is not.
Teacher certification is administered state by state, with its own rules on recognising out-of-country preparation, its own examinations, and often a requirement for coursework in state history or law. Some states have streamlined routes for experienced teachers; others do not. The gap between arriving with permission to work and being able to work in your own profession is where families lose a year.
Start the certification enquiry before the move, in writing, with the specific state's education department. Children in dependent status may attend school and may not work, and that status ends at twenty-one whatever the parent's classification.