Dependent status does not follow the corporate structure. A spouse and unmarried children under 21 may qualify for TD, with steps depending on each person's nationality, and TD permits study but does not authorize work, including remote work for a Canadian company.
Keep the company and the family status separate
A common assumption is that a spouse can keep billing through the family's Canadian company while in the United States on TD. TD does not authorize employment, and remote or unpaid work is not an automatic exception. If the spouse needs to work, that requires a separate basis in their own right. A child who is a US citizen does not need TD.
Record children's schooling plans and ages, and note whether the household intends to arrive together or in stages, since that affects each person's documentation needs. The record that settles a family issue is usually the marriage or birth record plus the principal’s status evidence, not an informal household plan. Each spouse applies on their own offer, their own credential and their own citizenship; a Canadian permanent resident spouse cannot use TN at all and would need a different route.
A Canadian citizen may apply at a port of entry without a visa stamp, or a U.S. employer may file Form I-129; TD dependants may study but may not work.