Yes. An E-2 spouse is employment-authorized incident to status and may work for the enterprise or anyone else. Children under 21 in E-2 dependent status may study but not work, and they age out at 21.
The spouse works; the children do not
Once the principal is admitted, the spouse's E-2 dependent status carries employment authorization without a separate application, and the admission record serves as evidence of it, though obtaining a card can simplify payroll onboarding. That means the non-principal spouse can be an employee of the roastery, draw a wage and, if desired, hold shares, without any effect on the principal's application. Two things still deserve care.
First, the principal must be the one who develops and directs the business, so the record should show her making the decisions the review associates with control, even if he runs the café day to day. Second, dependants' status follows the principal's, so if she stops directing the enterprise the family's status is affected together. Children may attend school but cannot take even part-time work, and their dependent status ends at 21, at which point they need a status of their own.
Hypothetical example: A Canadian couple opens a U.S. Pilates studio, with one spouse as the investor and the other planning to manage client scheduling. The file should identify who makes the high-level decisions and keep records showing the investor develops and directs the enterprise.
The dependent spouse's admission record settles work permission, while the operating agreement and payroll records settle the business roles. A first review also produces a family calendar for school enrollment and each child's twenty-first birthday. The business must remain a real, non-marginal operation; family work arrangements cannot substitute for the required enterprise evidence.