Her husband can. L-2 spouses are employment-authorized incident to status and may work for any employer. Children in L-2 status may study but not work, and lose dependant status at 21.
Spouse works incident to status; children study
Hypothetical example: If Ines's husband is a self-employed electrician in Logan Lake, he may take a U.S. job or open a U.S. business once admitted in L-2 status, without waiting for a separate employment document. USCIS treats L-2 spouses as employment-authorized incident to status and issues an admission record annotated to show it. He may still request an employment authorization document if a licensing board or employer wants one. Any state trade licence he needs is a separate professional-regulation matter. Their children may attend public school or college in L-2 status but may not work, including part-time jobs. Each child's status ends at 21 or on marriage. Everyone's status depends on Ines's L-1B remaining valid; if the placement ends early and the affiliate does not reassign her, the family's authorization ends when hers does, so the employer should say in writing what happens if the customer cancels.
Hypothetical example: A dental-laboratory CAD specialist transfers with a spouse who wants to open an online craft business and a child finishing secondary school. The family should obtain records showing the marriage and parent-child relationship, then plan the spouse’s work evidence separately from the child’s school enrollment. The principal’s approval controls the family’s period of stay. A business launch that depends on the spouse working should not begin before the appropriate admission evidence is available.