A spouse or unmarried child under 21 may qualify for TD, with steps that depend on each person's own nationality. TD permits study but does not authorize employment, and that stays true regardless of how the principal's travel is arranged.
Dependents' records are separate from the principal's
If dependents also move back and forth, each has an individual admission record with its own end date, which will not necessarily match the principal's. Check those records after each entry too. A spouse who spends long stretches in Canada does not gain work permission in the US by holding TD, and remote or unpaid work is not automatically outside that limit; that question belongs with counsel.
Choosing TD because an offer has not arrived yet is reasonable, provided everyone understands what it means in the meantime: study is permitted, employment is not, and there is no blanket rule allowing work while a later application is pending. Dependants hold TD status, which authorizes residence and study but no employment of any kind, and working remotely from inside the United States for a Canadian employer is still work performed there. The principal must independently hold Canadian or Mexican citizenship, credentials matching a listed USMCA profession, and prearranged professional work that excludes self-employment.