The investor's spouse is employment-authorized incident to status and may work anywhere, including in the business. Children admitted as dependants may study but may not work in it.
Helping out is still employment
Hypothetical example: the couple assume their eighteen-year-old son will staff the attended hours at weekends. He may not. A dependent child may attend school at any level but may not accept employment, and unpaid work in a family business is not a way around the rule. His mother, as the spouse of the principal investor, may work, and if she takes a paid role in the enterprise it has to be recorded properly in payroll rather than treated as helping out. Note also that the son's derivative status ends at twenty-one, and that treaty investor status does not itself lead to permanent residence, so a family expecting to remain indefinitely needs a separate plan. Payroll that includes people who are not authorized to work creates problems for the business as well as for the individuals.
Family businesses accumulate structure over decades: a holding company, a family trust for estate planning, shares issued to a spouse for income-splitting, an estate freeze that created several classes of shares. Each family member has their own application and eligibility, so approvals and appointments may not arrive together; schedule each worker according to their own applicable authorization, including any independent permission held.