She may enrol and study full time in TD status, but she may not take a campus job or any other employment. Work authorization is never available to a TD dependant; a job requires a status of her own, such as her own TN if she is a Canadian citizen in a listed profession.
Study yes, employment no, whatever the campus arrangement
TD status is granted to the spouse and unmarried children under 21 of a TN professional and expressly permits study, full time or part time, at any level. It does not permit employment in any form: a paid campus position, a graduate assistantship with a stipend, freelance work for Canadian clients performed from the United States or unpaid work that would otherwise be done by a paid employee. This is stricter than the L-2 and E-2 spousal rules, which authorize employment incident to status, and families sometimes assume the TN household enjoys the same treatment.
It does not. A spouse who needs to work has three realistic options: her own TN if she is a Canadian citizen and her occupation is listed, F-1 student status if her program qualifies and she needs its limited on-campus work permission, or a different employer-sponsored category. Children in TD may attend school through university age but face the same bar on work until they hold their own status.