Not from inside the United States. TD status permits a spouse and children to accompany the TN professional and to study, but it does not allow employment, whether for a U.S. customer or for his own Ontario company.
TD is a companion status, not a work permit
Hypothetical example: the nurse's husband runs a small electrical contracting business in South Frontenac and assumes he can keep invoicing Ontario clients from a house in New York. TD status does not authorize employment, and work performed while physically in the United States is U.S. work regardless of who pays or where the invoice is addressed.
Winding the business down, hiring a manager to run it while he is away, or keeping his own residence in Canada and visiting are all lawful options; running it from the U.S. kitchen table on TD is not. If he wants to work in the United States he needs his own category, and as a licensed electrician without a degree he is unlikely to fit a TN profession, so the honest answer may be that his route is different from hers or does not exist yet.
The children may attend school on TD without a separate student status. Put each family member's intended activity and physical work location on a calendar before anyone moves. Hypothetical example: a Canadian museum conservator accepts a TN position while her spouse owns an online antique-map shop.
The spouse may visit Canada to pack orders or arrange a different work-authorized classification, but operating the shop from a U.S. home on TD is not permitted. The decision is whether the household can separate those activities in reality, not whether customers pay in Canadian dollars.