A TD dependant may not be employed in the United States. 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. Ask counsel before the household relies on that income.
What TD does and does not allow the household
The rule itself is short: dependants admitted in TD status may study but may not work in the United States. What that means for a person who owns a stable in Erin and answers its email from a kitchen in another country is genuinely less clear, because the prohibition is about employment in the United States rather than about the location of the customer. Some households manage the risk by having the Canadian business run day to day by an on-site manager, with the spouse holding only an ownership interest and taking distributions rather than a salary for services performed while present.
Others conclude that the income matters enough to justify the spouse seeking her own status. The one approach that reliably causes trouble is assuming the question does not exist. Children in TD status may attend school.
Every dependant's admission is tied to the principal's, so if the principal's TN ends, the household's status ends with it, and a nineteen-year-old who wants paid work needs his own basis for it.