Yes. An E-2 spouse is employment-authorized incident to status and is not restricted to the treaty enterprise, so a spouse may take unrelated employment. Children admitted as derivatives may live and attend school but hold no work authorization, and they cease to qualify at 21 or on marriage.
One household, two different sets of permissions
The spousal rule is unusually flexible and is worth planning around when the business is seasonal. If the resort generates income for five months, Saoirse's ability to take a job elsewhere in the community during the quiet half of the year is not an immigration problem, and it can be the difference between a viable household budget and an unviable one. Children are treated differently.
Derivative status lets them live in the United States and attend school, but confers no permission to work, so a nineteen-year-old cannot take a summer job at the family's own resort on that status. The age limit applies continuously: at 21 the derivative relationship ends, whatever the parents' status, and a young adult intending to remain needs a basis of their own arranged in advance. Because E-2 offers no direct permanent route, a family expecting to settle should take advice about that separately.