TD status does not authorize employment, and remote work performed from inside the United States is generally treated as work in the United States even when the employer and clients are Canadian. He should not plan on it without his own status.
Treat remote work as work, and find him his own route if he needs one
Hypothetical example: her husband is a payroll administrator for an Edenwold logistics firm that would happily let him work from a laptop in the United States. The employer's flexibility does not change the law: TD dependants may study but are not employment-authorized, and counsel generally treats productive work performed on U.S. soil as employment regardless of who pays. Three honest options exist. He can take leave or resign and study, which TD permits. He can remain in Canada and visit. Or he can look for his own route; a payroll administrator is unlikely to fit a listed TN profession, but if his employer has a U.S. affiliate and he has a year of qualifying service, L-1 might be examined. Their children may attend school as TD dependants. Budget the ten months on her fee income alone until a lawful basis for his work exists, and align everyone's admission period with hers.
Hypothetical example: a biologist on TN wants her spouse and a 20-year-old unmarried son to join her after she begins work. The marriage certificate, the son's birth certificate, and each person's passport settle the family relationship question; the son's age on admission matters. Decide whether they will travel with her or later, then keep copies of her I-94 and employment letter for their applications. Her employer may use a port-of-entry TN request or Form I-129, but TN does not authorize her to operate a business for herself.