Yes, if she is admitted as his E-2 spouse. Employment authorization for a qualifying E spouse arises incident to status, evidenced by the annotation on Form I-94, and she may work for any employer or for herself. Children under twenty-one may study but not work.
The spouse can take any work; the children cannot take any
This asymmetry catches families with older teenagers. A qualifying E-2 spouse needs no separate employment authorization document before starting a job, which means she could work in the forage company's office, take unrelated employment or run her own business. Her own nationality does not matter for dependent status, so a spouse who holds Canadian permanent residence rather than citizenship still qualifies as a spouse.
Unmarried children under twenty-one may attend school and may not work at all, including summer jobs. On reaching twenty-one a child must obtain an independent status. One further point shapes long-term planning: E-2 is granted in renewable periods for as long as the enterprise continues to qualify, but it carries no direct path to permanent residence.
A family hoping to settle permanently should raise that with a licensed U.S. immigration attorney separately.