An L-2 spouse is employment-authorized incident to status and may work for any employer, including the U.S. subsidiary. His employment there should be genuine and paid, and it does not affect the analysis of your own managerial role.
L-2 work is open, but keep it separate from the petition
Hypothetical example: the husband of a Rothesay logistics vice-president is a diesel mechanic and would like to run maintenance at the U.S. terminal. Once admitted in L-2 status he is employment-authorized incident to that status and may take that job.
The subsidiary should employ him on the same terms as any other mechanic, with payroll and tax withholding, because informal or unpaid arrangements create questions later. His employment should not be used in the L-1A petition as evidence of her management, since the petition's organization chart should reflect the staff she directs independently of family. If the couple expects his work to lead to his own long-term status, that would require a separate analysis; L-2 status depends on hers and ends when hers does.
Their child may accompany as an L-2 dependant until age 21.