His spouse and unmarried children under twenty-one may accompany him in L-2 status. The spouse is employment-authorized incident to status and may work for any employer or run her own business; the children may study but not work.
The L-2 spouse's position is strong, but the children's is time-limited
Families usually get one thing wrong in each direction. They underestimate the spouse's rights, assuming she needs a separate application to work, when an L-2 spouse's employment authorization is incident to her status and is evidenced by her admission record. And they overestimate the children's position, assuming a child can take a part-time job or stay in L-2 status through university.
A child loses dependant eligibility at twenty-one or on marriage and then needs a route of his own, typically student status through a certified school. Plan that transition early; a child who is nineteen at the time of transfer will need his own status within two years. Health coverage, school enrolment and a driver's licence follow from the family's admission records, so keep each person's I-94 record accessible.
If the spouse intends to practise a licensed occupation, immigration permission is only the first step; state licensing is a separate matter with its own timeline.