TD does not authorize work. A principal’s revised job description does not grant a dependent an employment benefit.
Review household consequences separately
Check the actual status and proposed activities of relatives. A private employer amendment is not an individual admission record. The dependent category is for a qualifying spouse or unmarried child under 21; each person needs valid status.
TD exists so that a professional's household is not separated by the assignment, and it is generous about presence: the dependant is admitted for the same period, may come and go, and may enrol in school or a college program. Whether operating a Canadian business remotely while physically present in TD status counts as prohibited employment is not clearly settled, and the safe assumption is that it may be treated as work. TD dependants may enrol in study, full-time or part-time, but they may not accept employment in the United States, and no length of residence, no school enrolment and no employer goodwill alters that. Review any proposed remote activity or unpaid role specifically, and consider an independent work-authorizing route where relevant before relying on a second income.