Dependants' status follows the principal's. If the principal's petition is affected by a restructuring, the spouse's employment authorisation and the children's status are affected at the same time.
One petition supports the whole household's permission
An L-2 spouse is employment-authorised incident to status, which is a significant practical benefit, and L-2 children may attend school though they may not work. All of this depends on the principal continuing to hold valid L-1 status. If a restructuring undermines the qualifying relationship, or if the transferee's role drifts away from managerial duties, the consequences reach every member of the household at once, including a spouse who may by then have her own employer and a mortgage.
That is a reason to treat the amended-petition obligation seriously rather than as paperwork. It is also a reason to note each child's twenty-first birthday, since dependent status ends there regardless of how long the assignment runs, and the seven-year L-1A maximum should be marked on the same page.