Yes. An E-2 spouse is employment-authorized incident to status and may work for the enterprise or any other employer; children may study but may not work.
The spouse can work anywhere; the children are limited to school
Hypothetical example: The spouse of a Portugal Cove-St. Philip's E-2 investor is admitted in E-2 dependant status and, under current USCIS policy, is authorized to work incident to that status; the admission record annotated as an E-2 spouse serves as evidence of employment authorization. The spouse may therefore take over the contracting company's bookkeeping and scheduling, or take an unrelated job, or work remotely for a Canadian client. Whether the spouse's nationality matters for the dependant status does not depend on the spouse being Canadian; the treaty nationality requirement applies to the principal investor and the ownership of the enterprise. Children under 21 may attend school as E-2 dependants but have no work authorization, and they lose dependant status on their 21st birthday, which for a family with an older teenager should be planned around from the outset. Because E-2 does not itself lead to permanent residence, a child who wants to remain long-term will eventually need an independent basis.
Hypothetical example: a Canadian investor opens a specialty tea-import business and the spouse expects to manage its online orders while a nineteen-year-old child plans to work weekends. The household should make one activity list for each person before travel: paid management, inventory work, school, and future employment. The admission records and each person's age settle what is authorized, not a shared ownership interest or family intention. If the child's planned work is important to the forecast, revise the staffing plan now rather than rely on unpaid family labour that cannot lawfully perform the role.