TD status does not authorize employment, and where the work is physically performed matters more than who pays. Nursing is not remote work in any case, so this needs its own route.
Each spouse needs a category that permits the activity
Hypothetical example: the husband of a Quispamsis TN applicant is a licensed practical nurse who expects to fly back for occasional shifts and otherwise stay in the United States as a TD dependant. TD permits study but not employment, and the occasional-shift plan raises its own admission questions each time he crosses. If he wants to work in the United States, the relevant question is whether he can qualify independently: the TN Registered Nurse listing accepts a state or provincial licence or a Licenciatura Degree, and a practical-nurse licence is a different credential from an RN registration, so the listing may not fit.
He should confirm with the state board what registration he could obtain and whether an employer would sponsor him in his own right. Until then, his U.S. activity is limited to what TD status allows.