Yes. A spouse admitted in L-2 status is employment-authorized incident to that status. Children admitted as derivatives may attend school but are not authorized to work on that basis, and derivative eligibility ends at twenty-one.
The spouse's rights are broad; the children's are not
Hypothetical example: the director's spouse manages a small bookkeeping practice in Coaldale and expects to look for work in the United States, while their nineteen-year-old plans to study and take shifts somewhere. The spouse's position is straightforward once admitted in L-2 status, since employment authorization comes with the status itself, and the evidence of status is what an employer will want to see. The nineteen-year-old is in a different position: study is permitted, employment is not, and any job would need its own lawful basis such as a student route with its own restrictions.
Note the ages against the length of the assignment, because a seven-year maximum in L-1A status outlasts a nineteen-year-old's derivative eligibility. Check each family member's citizenship as well; a family member who holds Canadian permanent residence rather than citizenship may face different procedural steps than the principal.