Yes. An E-2 spouse is employment-authorized incident to status and may work for any employer. Unmarried children under twenty-one may accompany the family and may study, but they may not work.
Spousal work is allowed; the children's clock still runs
Employment authorization incident to status means the spouse does not depend on a separate application before taking a job, which for many families is the difference between a workable move and an unworkable one. Children in derivative status may attend school. Their eligibility ends at twenty-one, and E-2 offers no direct route to permanent residence, so a family with older teenagers should think about what happens after a child ages out rather than discovering it later.
One further point specific to Anouk's situation: if she intends to keep operating the Nipissing construction firm while directing the U.S. company, her own presence and time commitment in each business should be planned honestly, because develop and direct is a real obligation rather than a title, and the family's own arrangements will follow from it.