Not through the first partner’s E-2 case merely because the other person owns the business. The other household needs its own valid basis for residence and work; that could involve its partner’s qualifying E case or an independent route. Business ownership alone does not confer derivative benefits, and some other statuses may provide their own work authorization.
Decide which household is relocating first
List, per family, who is moving and whether that household's income depends on a spouse working. A qualifying E spouse is generally employment-authorized incident to valid status; confirm the proof actually available, such as an E-2S notation or the I-94 record, before anyone accepts a job offer. Dependent children get no work authorization from their status. If the second partner also needs to be in the United States, ask what basis would apply to that person.
A legally married spouse and unmarried children under 21 may accompany you, each through their own process; approval dates are not shared and are not guaranteed to align with yours. The principal must show treaty nationality, qualifying enterprise nationality, irrevocably committed at-risk funds, substantiality, a real nonmarginal operation, and development and direction through half ownership or operational control.