Yes, your spouse and unmarried children (20 years old and below) can accompany you or follow to join at a later time as your dependents as Derivative E-2 visa applicants. There is no requirement that their nationality be the same as your required nationality for the E-2 Treaty Trader Visa.
This is something you should discuss in details with your US Business immigration lawyer. The US Business immigration consultancy firm presenting your business would only present the E2-Investor applicant and none of the Derivative E-2 visa applicants.
Disclaimer: Any information contained in this website & chat is provided for general guidance only, and is not intended to be a source of legal advice. As such, any unlawful use is strictly prohibited. Prior success does not guarantee a similar outcome.