Yes. An L-2 spouse is employment-authorized incident to status and may work for any employer, including the family's subsidiary. L-2 children may study but may not work, and the whole family's status ends with the principal's.
The spouse's authorization is real, the children's is not
Since USCIS confirmed that L-2 spouses are employment-authorized incident to status, a spouse admitted in L-2 status with the correct annotation on the I-94 may start work without applying for a separate employment document. The spouse could therefore handle the subsidiary's bookkeeping, dispatch or estimating, and be paid, provided the spouse's status is valid and unexpired. The family's teenagers hold L-2 status too, and may attend school, but cannot take a summer job on the crews or anywhere else.
Two limits should be written into the household plan: the spouse's authorization lasts only as long as the principal's L-1A status, which is capped at seven years in total, and if the couple divorces the L-2 status ends. If the spouse also holds a qualifying role in the Canadian company, an independent L-1 can be assessed, but it is not needed merely to work.