Under the official framework each person's participation carries its own processing fee, and the treatment of a spouse and children in the corporate-sponsored route should be read on the official page rather than assumed. Derivative family members in an employment-based immigrant case ordinarily include the spouse and unmarried children under twenty-one, but the financial terms for each must be confirmed.
Confirm the per-person terms and the age deadline
Two questions need separate answers. The immigration question is whether the husband and children can immigrate with her as derivatives of an employment-based immigrant case; in the usual EB-1 or EB-2 framework a spouse and unmarried children under twenty-one can, subject to age-protection rules for a child approaching twenty-one. The financial question is what the sponsor will pay for them.
The official program page states that each family member is subject to an additional US$15,000 DHS processing fee and US$1 million gift. Ask the sponsor directly whether it will fund the family members or only the principal, and whether the family's amounts become repayable if she leaves. Re-verify those terms on the official page before any money moves.
Until permanent residence is granted, the husband cannot work in the United States on the strength of the pending case, and the children may not enrol in US schools as if resident; visits remain visits.