A spouse and unmarried children under 21 can seek TD status. They may attend school but cannot work, and a spouse's remote job for a Québec employer counts as work while physically in the United States.
Plan around the no-work rule, not against it
TD status is derivative: it exists because the principal holds TN, and it ends when TN ends. Dependants in TD can study full time without changing status, which usually covers children and often a spouse who wants to pursue a program. What TD does not permit is employment of any kind, and that includes continuing a remote position for an employer in Sainte-Catherine-de-la-Jacques-Cartier or elsewhere in Canada while living south of the border.
A spouse who needs to work should have their own route assessed, whether that is a TN in their own profession, another employment category, or a decision to remain in Canada for part of the year. Record the children's birth dates; a child who turns 21 loses TD eligibility, and marriage ends it regardless of age. Bring marriage and birth certificates, with translations, for each dependant's own application.