Yes. The spouse of an E-2 treaty investor is employment-authorized incident to status and may accept employment without a separate work permit. Unmarried children under 21 may hold derivative status and attend school but may not work.
Employment for the spouse, study for the children, permanence for nobody
Households frequently plan around the spouse's earnings, which is reasonable, and then forget the second half of the sentence. Derivative status for a child ends at 21, and a child who has spent years in the United States as a dependant does not gain any residence right from that time. Because E-2 has no direct path to permanent residence, a family that intends to stay indefinitely is relying on a status that must be maintained and renewed as long as the investment continues and qualifies.
Selling the chip-hauling business, or reducing Fatima's ownership below the level that lets her develop and direct it, unsettles everyone's status at once. That dependency is worth naming out loud before children are enrolled and a Canadian house is sold.