Yes. An E-2 spouse is employment-authorized incident to status and may work in the nursery or anywhere else. Unmarried children under 21 hold E-2 dependant status and may attend school, but they may not work, including at the family business.
The spouse works; the children study only
Hypothetical example: a Haldimand County couple buys a U.S. garden centre; the investor spouse will manage growing and purchasing, the other spouse will run the retail counter, and two teenagers will attend the local high school. The second spouse's role is straightforward: E-2 spouses are authorized to work by virtue of their status and can be on the payroll, though many obtain an employment authorization document as a convenient proof for payroll and licensing.
The teenagers can enrol in public or private school as E-2 dependants. What they cannot do is take shifts at the garden centre, even unpaid, since dependant children have no work authorization; a seasonal helper role must be filled by U.S. workers.
Their status ends when they turn 21, and E-2 provides no path to permanent residence, so a child approaching that age should have a plan, such as a student category, in place well before the birthday. Record each family member's role in the business plan accurately; officers do read it.