No. TD never authorizes employment, and status cannot be changed casually once the family has settled. A nurse who intends to work should be assessed for a TN of her own before the move.
Two professionals means two separate TN files
TD status is available to the spouse and unmarried children under 21 of a TN professional, and it permits study but not work in any form. A registered nurse is a listed profession with its own credential rule, a state or provincial licence or a licenciatura degree. U.S.
practice requires the applicable state nursing authorization, and health-care-worker certification may also be required for admission; an employer may make an offer contingent on completing those steps. Because these steps can take time, the nurse's plan should start when the engineer's does, not after arrival. Each spouse applies on their own offer, their own credential and their own citizenship; a Canadian permanent resident spouse cannot use TN at all and would need a different route.
Children in TD status may attend school. If the nurse will not work in the first year, TD is appropriate, but say so deliberately rather than by default.