Yes. An E-2 spouse is employment-authorized incident to status and may accept employment without a separate grant of permission. Children may live and study in derivative status but may not work, and their eligibility ends when they turn twenty-one.
The spouse's freedom is often the deciding feature
For a household considering an investment route against an employment route, the spouse's position is frequently what settles it. Employment authorization incident to status means the spouse is not confined to the family business and may take unrelated work, which matters when a new enterprise cannot yet support two salaries. Practical preparation still helps: American employers vary in what they ask for, and it is worth knowing before an offer is made how the authorization will be evidenced.
For children, the position is narrower. Study is permitted at any level, employment is not, and there is no derivative status after twenty-one, so a household with a teenager should map that date against the expected life of the business. It is also worth remembering that the whole structure rests on a nonimmigrant status tied to a continuing enterprise, not on residence.
Households sometimes assume a temporary classification eventually converts into something permanent. This one does not, so a long-term intention needs an immigrant route found on its own merits.