Not on TD status, which does not authorize employment. Secondary-school teaching is not a listed TN profession, so she would need to qualify under a different category in her own right. TD allows study for spouses and unmarried children under 21.
TD permits study but does not authorize employment; secondary-school teaching is not on the TN list
The TD spouse and children of a TN professional may live in the United States and attend school, but no TD dependant may work. Hypothetical example: a Sainte-Brigitte-de-Laval secondary-school teacher wants to work while accompanying a TN spouse. The Appendix 2 list includes college, seminary and university teachers, but not primary or secondary teachers, so the teacher cannot obtain TN on the strength of that profession.
The realistic options are to use the period for study, which TD permits, to seek a different U.S. employer-sponsored category if an employer will petition, or to remain in Québec. Tutoring, online teaching for a Canadian school, or paid substitute work are all employment and are not allowed on TD.
Children under 21 may attend school at any level and lose TD status at 21 or on marriage. The household should decide before acceptance whether one income and a study plan is workable, because the immigration rules will not adjust afterwards.