The husband can hold L-2 status and is employment-authorized incident to that status, though a state teaching licence is a separate matter. The son qualifies as an L-2 dependant only while unmarried and under 21, so his status ends at his birthday unless he has another basis to remain.
The spouse can work; the son is on a clock
Hypothetical example: a Haldimand County feed-mill manager is moving under L-1A with her husband, an Ontario-certified teacher, and their twenty-year-old son. The husband's position is favourable: L-2 spouses are employment-authorized incident to status, so he can accept a job without a separate work permit, though he may need an employment authorization document as proof for some employers and will need whichever state teaching credential the school district requires. The son's position is time-limited.
Dependant children must be unmarried and under 21; when he turns 21 his L-2 status cannot be extended, and he must either depart, change to a status of his own such as a student category, or have left before that date. If the family's longer plan involves permanent residence through the manager's executive role, his age at that filing also matters under the Child Status Protection Act rules. Put his birth date on the timeline first and plan the rest around it.