He may continue to own the shop, but managing it while physically in the United States in TD status is work, and TD does not authorize employment. Directing staff from abroad is a different fact pattern from owning shares.
Ownership is not the problem; activity is
TD status is available to the spouse and unmarried children under 21 of a TN professional. It permits study and residence, and it does not permit employment, whether for a U.S. employer, a Canadian employer or the dependant's own business.
A spouse who owns a Mount Pearl repair shop can remain the owner, receive distributions and sign documents as shareholder. Day-to-day management from a U.S. address, such as scheduling technicians, approving invoices and dealing with customers, is activity that TD does not cover.
The practical choices are to appoint a manager in Mount Pearl and limit his involvement to owner decisions, to have him remain in Canada for part of the year while the family relocates, or to review whether his own qualifications support an independent route. Children can enrol in school on TD. If the spouse is a permanent resident rather than a citizen, TD remains available to him as a dependant, but he cannot obtain TN in his own right.