A spouse and unmarried children under twenty-one may qualify for TD, and their status depends on the principal's TN status and the family relationship rather than on where the principal is working in a given week. Rotations do not change that, but they change household planning considerably.
Plan for the household when the principal is away
TD permits study and does not authorize employment, so a spouse cannot take paid work to fill long stretches alone, including remote work. Consider where the family will actually live relative to the field program, whether children's schooling is settled, and what documents each family member needs, since the steps differ by nationality. A child who is a United States citizen does not need TD at all.
Hypothetical example: a geochemist works four weeks on and two weeks off, so the household spends most of the year with one adult present. Decide where the family will actually be based before signing a lease near the field program, since a camp-based rotation rarely justifies living beside it. Settle the practical questions the rotation creates: who can sign for a child at school, how medical coverage works during the absences, and what happens to the household if the principal's status changes mid-rotation.
Write down each member's citizenship and the document each would present, because the steps differ by nationality and are easier to sort out now than during a mobilization week. If a spouse intends to work eventually, treat that as its own question with its own filing, not as something that follows from the principal's status.