TD status does not permit employment, and remote work for a Canadian employer performed from U.S. soil is still work in the United States. The spouse needs a status of their own that allows it.
Location of the keyboard, not of the payer, decides it
TD is available to the spouse and unmarried children under 21 of a TN professional, and it allows study but not employment. The common misunderstanding is that a salary paid in Canada by a Canadian employer sits outside U.S. rules. It does not: the activity is performed in the United States, so it is U.S. employment for immigration purposes regardless of where the payroll runs. A spouse who wants to keep a professional job should look at their own eligibility, for example a separate TN in a listed profession with their own employer letter, or another category that authorizes work. Children in TD may enrol in school. Each family member needs their own passport, proof of relationship and, where relevant, evidence of the study or activity intended.
Family planning starts with each person's status, not with a shared mailing address. The TN professional should carry proof of the marriage and of each child's age; a dependant's passport and admission record should be checked separately after arrival. TD permits study, but it does not authorize employment, including work performed remotely while physically in the United States. A spouse who needs employment should evaluate an independent category before moving. Hypothetical example: a veterinary pathologist accepts a TN role while her spouse operates an online stationery shop. The shop's ongoing sales do not make TD work permissible, so the couple must choose a lawful work category or keep the spouse outside the United States while operating it.