That is a household decision worth taking deliberately. A new operation carries more uncertainty than an established one, and an initial period of authorization may be shorter than the family expects. Eligible spouses and unmarried children under twenty-one may seek dependent status; children are not work-authorized by it.
Consider a staged move
Some households send the transferee first and follow once the operation has settled, which trades separation for flexibility. Others move together to avoid a second disruption. Neither is wrong.
What matters is that the family understands the operation's stage before committing to schools, housing, or a partner's resignation. Ask counsel how a spouse's employment authorization would work here before treating it as settled. One condition should be settled before the household chooses.
Dependent status is available to a spouse and unmarried children under twenty-one, and a spouse in valid L-2S status is generally employment authorized incident to that status, while children are not work authorized by it. If the household budget assumes a spouse's earnings, confirm what evidence a United States employer will ask to see and how long that evidence takes to obtain, because the practical question is not whether authorization exists but when it can be demonstrated. Where a staged move is chosen, note that bringing dependents later is a separate step with its own preparation and its own documents.