No. TD dependants may accompany the TN holder and may study, but they cannot accept employment. Anyone in the household who wants to work needs a status of their own.
The dependant category is the constraint, not the person
Hypothetical example: the planner's spouse runs a small residential landscaping business and assumes she can carry on working after the move. She cannot work in the United States in TD status, and the answer does not change because the customers or the paying employer are Canadian; the physical location of the work is what matters, and it is worth raising before anyone gives notice. Her realistic options are a status of her own — a professional position in a listed profession, an employer petition, or a student route — assessed on her own facts rather than on her husband's. Children admitted in TD status may attend school. They also age out: derivative eligibility ends at twenty-one, so a child's birthday belongs on the planning calendar from the first week rather than being discovered during an extension.
Hypothetical example: an airport land-use planner's spouse plans to continue a remote bookkeeping practice after moving. The first review should list each family member's intended activity, citizenship, age, and planned location while doing it. Passports and birth records settle identity and age; the proposed work arrangement settles whether a separate authorization is needed. Sequence the family review before resignations, school enrollment, or client commitments. The recurring mistake is treating payment from abroad as permission to perform work while physically in the United States. A dependent child's school plan and a spouse's income plan require separate answers.