The spouse may enter in L-2 status and is employment-authorized incident to that status, so no separate work permit is required before accepting a job or working independently. Occupational licensing, professional registration and tax registration are separate matters with their own requirements.
Work authorization and permission to practise are different questions
Households repeatedly conflate the two. A spouse in L-2 status may lawfully be employed, and that answers the immigration question completely. It does not answer whether the state in question will let her practise her occupation, register a business or bill clients, and where her field is licensed those approvals run on their own timetable and can take longer than the assignment itself is scheduled to last.
Anyone planning to keep a career moving during eighteen months abroad should look at that timetable before the family commits. The dependent rules themselves are the same regardless of which L category the principal holds: unmarried children under twenty-one may accompany the family and attend school without working, and every dependent status ends when Solveig's does. A child approaching twenty-one needs an independent route arranged in advance.