Yes. An E-2 spouse is employment-authorized incident to status and may work for the enterprise, another employer or herself. Children in E-2 status may study but are not authorized to work.
The spouse's work is not limited to the family business
The spouse of a treaty investor is admitted in E-2 dependant status and, under current policy, is considered employment-authorized incident to that status, with the annotated admission record serving as evidence for employers. She may join the parts distributor as bookkeeper or manager, take an unrelated job, or start her own activity; none of those choices needs a separate authorization document, though some spouses obtain one for convenience. Children under 21 may attend school and may not work, and a child who turns 21 must have a separate basis for staying. Because E-2 does not lead directly to permanent residence, a family planning a long stay should note that children who age out cannot simply be added back later. The spouse's own citizenship does not matter for dependant status, but if she is also a Canadian citizen and holds a share of the business, her ownership counts toward the Canadian-ownership requirement. The family's status lasts as long as the principal's, so the business's continued qualification supports everyone's stay.
Hypothetical example: a specialty-coffee importer will be owned by a Canadian investor whose spouse plans to work for an unrelated publisher. The admission record settles the spouse's E-2 dependant classification, while the ownership register settles whether the spouse's shares help satisfy the nationality analysis. The couple should decide whether the spouse will hold equity before filing and document the actual payment for it. A child nearing 21 needs a separate education or immigration plan; family inclusion does not continue automatically after ageing out.