Not in TD status. TD permits residence and study only, so a spouse who needs to work should either qualify for a status of his own or the household should consider whether a different route for the principal, such as L-1, would give the spouse work authorization.
TD is the reason to ask the spouse's question first
The spouse and unmarried children under 21 of a TN professional may be admitted in TD status, which allows them to live in the United States and to study but not to work for anyone, including remotely for a Canadian employer while physically present. A paramedic could not practise, take a related job or drive for a service. He could enrol in a program, and the sixteen-year-old could attend high school.
If the household needs two incomes, the options are for him to qualify independently, which for a paramedic is difficult because the profession is not in Appendix 2, or for the developer to be employed in a way that genuinely supports L-1B or another status where the spouse is work-authorized. That is why this site places the spouse's work question ahead of the principal's route. The household should resolve that issue before choosing TN.