A spouse in L-2 status is employment-authorized incident to that status. Unmarried children under 21 in L-2 status may study but are not work-authorized through L-2, and each person's eligibility is assessed on their own passport and relationship evidence.
How to sequence it
Sequence the family's paperwork behind the principal's approval but not so far behind that it stalls the household. Hypothetical example: a Lévis insurance group transfers its U.S. finance director; his spouse is a self-employed bookkeeper and their son is nineteen and part-way through a college diploma.
The spouse's L-2 status carries employment authorization incident to status, which means she may work without waiting for a separate card, though she should check what documentation a given employer will accept. The son may finish his studies in L-2 status but cannot take paid work on that basis, and when he turns 21 he loses derivative eligibility and needs a status of his own. Plan his transition now rather than in the month he ages out.
Gather birth and marriage certificates and every passport at the start, since a missing document for one dependant should not delay the principal's filing.