Family planning follows the same logic as any TN case: dependents would travel on a status without independent work authorization, and timing should wait for the underlying employment and profession questions to be resolved first, since a project-based structure carries a real chance of not qualifying.
Avoid committing the household to an uncertain structure
Because the employment relationship itself is a live question in this scenario, hold off on firm relocation dates for a spouse or children until that question is answered. If the review concludes the arrangement is closer to independent contracting, the household's plans may need to shift toward a different route entirely, not just a delayed TN filing. Sequence the household decisions against the status decisions, not against the design schedule.
Dependants of a TN professional are admitted in a dependent status that carries no work authorisation, so a spouse who needs to earn should be assessed on their own facts and may need an entirely separate route. School enrolment often carries the earliest deadline in the household and the least flexibility, so identify it now and treat it as the fixed point around which other dates move. If the structural review concludes the arrangement is closer to self-employment, the family plan changes rather than slips, and that conversation is better held before deposits on housing or a school place have been paid.