No. TD does not authorize employment, including remote work performed while physically in the United States.
Review individual permission separately
A new benefits package does not change the spouse’s status rules. Identify actual proposed activities and current documentation.
A short, fixed-term assignment changes the calculus for a household move: a spouse and children could face a shorter stay tied to one academic term, without independent work authorization for a spouse under a dependent status. Build a dated review file around each dependent's passport, admission record, daily activity, school plans, and proposed paid work. Review each family member’s citizenship and intended activity; shared surnames are neither the entire proof of relationship nor a shared work authorization. Dependants' own status would follow whichever classification the applicant ultimately qualifies for, and those categories differ in what they offer a spouse and in what documents each person needs. Dependants of a TN professional are admitted in a dependent status that carries no work authorisation, so a spouse who needs to earn should be assessed on their own facts and may need an entirely separate route.