TD status permits study but not employment, so a nurse who arrives on TD and starts work is working without authorization. Registered Nurse is a listed profession whose Appendix 2 qualification is a state or provincial licence or a Licenciatura degree; she also needs her own employer letter and must meet any separate state licensing requirements.
Start the spouse's licensing before the move, not after
The usual error is sequencing. The principal applicant's TN is settled at the border in an afternoon, the family moves, and only then does the nurse discover that her state licence application will take months and that she cannot work meanwhile. The Registered Nurse entry may be met by a state or provincial licence or a Licenciatura degree; separately, the destination state and a US employer may require state authorization to practise.
Those steps should begin while the family is still in Canada. Until they are complete she may accompany her husband as a TD dependant, study, and prepare, but she should not accept shifts, casual work or agency placements. Their nineteen-year-old can hold TD status while unmarried and under twenty-one and may study, but if he intends to remain in college in the United States past that age he needs his own student status through a school certified by the Student and Exchange Visitor Program.