Dependents in TD derive their status from the principal, so an unresolved question about the principal affects them. TD permits study but does not authorise work of any kind, and remote or unpaid activities require individual review, so a spouse cannot lawfully replace the lost income on TD status alone.
Do not solve the income gap with TD
This is the point where households are most tempted to improvise. A spouse taking on paid work, or unpaid work for a company that expects to hire them later, is not permitted on TD, and remote work for an employer elsewhere is not a casual exception. If a spouse has, or could obtain, their own separate work authorisation, that is a distinct question for counsel.
A child who is a United States citizen needs no TD. Ask for the spouse's own admission record rather than assuming it mirrors the principal's, because the dates on the two documents are not always the same and a household plan built on the wrong date is built on nothing. Write down, for each family member, the document that proves their current period of stay and where that document physically is.
Study for a child generally remains permitted, so school arrangements are usually the least fragile part of the plan. Hypothetical example: a household discovers that the dependent record shows an earlier end date than the principal's, which changes what has to be filed and when.