The principal investor develops and directs the enterprise. A spouse admitted in E-2 status is employment-authorized incident to that status, which permits work. Children admitted as derivatives may attend school but are not authorized to work on that basis.
Two roles, and only one of them is the investment
Hypothetical example: one spouse will manage the shop and the other intends to keep driving, initially for an American carrier. The investor's obligation is to develop and direct the enterprise, so if the driving spouse is named as the principal investor while spending the week on the road, the file has a problem that no amount of paperwork solves. Decide who the investor is by reference to who will actually run the business.
The other spouse's employment authorization comes with E-2 status once admitted, though a commercial licence, medical certification and endorsements are separate regulatory matters. Note that E-2 provides no direct path to permanent residence, so a family intending to settle indefinitely should raise that at the outset rather than after the shop is bought.