Yes. A spouse of an E-2 investor is authorized to work incident to status, and that includes working in the family's own enterprise. Children in dependant status may study but not work in the business.
Spousal work is permitted; the children's is not
Hypothetical example: a Mission couple plan that he will run the technicians while she handles dispatch, invoicing and bookkeeping. Her E-2 dependant status carries employment authorization from admission, so she may take that role, be on payroll or hold shares, and even work for an unrelated employer if she prefers. Their seventeen-year-old cannot be put on the schedule to answer phones, because dependant children have no work authorization, and a child's status also ends at twenty-one.
The spouse's status depends on the principal's, so if the enterprise fails and his E-2 ends, her authorization ends with it. Couples who need her income to be independent of the business should say so at the planning stage, since a separate classification of her own might be more robust than reliance on derivative status. Hypothetical example: An E-2 investor in a mobile pet-grooming business plans to have a spouse manage bookings and a college-age child operate a second vehicle.
The family review should identify which person will work, hold shares or merely accompany the investor. A properly admitted E-2 spouse may work, but a dependent child may study and is not employment-authorized by that status. The business records should match the plan: payroll, ownership entries and job descriptions must not quietly place the child in productive paid duties.
If the child needs work permission, decide on an independent classification before expanding the business around that role.