Each person’s actual status and documentation require review. The principal’s records do not establish every dependent’s admission, stay or work permission.
Compare individual family records
Qualifying L spouses are employment authorized incident to status with appropriate documentation. Children gain no work permission solely through L dependent status. Review individual categories and dates rather than assuming the family received identical records.
For each dependant, ask which of them needs something the principal's file does not already produce. A spouse who intends to work needs the documentation appropriate to employment authorization incident to status, and that is a separate item to assemble rather than a consequence of the principal's approval. A child needs nothing for work, because L dependent status confers no work permission, but does need their own admission record checked against their own passport.
A dependant who travelled separately, or entered on a different date, will have a different record and possibly a different date; assuming otherwise is the common failure. Build the list person by person and mark, for each, whether their permitted stay is tied to the principal's and what happens to it if the principal's dates are corrected. That table is more useful to a household than any general explanation of dependent status.