Yes. An E-2 spouse is employment-authorized incident to status and may work for any employer or in the rental business itself. Unmarried children under 21 may study in E-2 derivative status but may not work, and lose that status at 21.
Household planning around a franchise
The spouse's authorization does not depend on the franchise and does not need a separate application beyond obtaining E-2 derivative status; the spouse should carry documentation evidencing that status for an employer's records. If the spouse is the household's accountant, for instance, she may work in the business, for a U.S. firm or for anyone else.
Children may enrol in school. The date each child turns 21 should be written on the plan, since derivative eligibility ends then and a student category or other basis must be arranged beforehand. The spouse's own nationality does not matter for derivative status, though a spouse holding only Canadian permanent residence follows a different consular process from a citizen.
E-2 is a nonimmigrant category with no direct route to permanent residence, and a family that hopes to settle should raise that at the first review rather than after several renewals. The Québec contracting business also needs a plan for his absence, which is a commercial question.