CHF does not guarantee sponsorship of J-2 visas for dependent relatives nor work permits for spouses.
J-2 work permits have becoming increasingly difficult in recent years, as the Department of Homeland Security (DHS) only issues EAD (Employment Authorization Documents) for a 2-year period, and the waiting time to receive approval has lengthened from 6 to as long as 9 months since the Covid epidemic and the shutdown or reduction in staff in many USCIS offices that consider and approve applications:  Form I765 link:
https://www.usimmigration.us/employment/authorization

When requesting a work permit, the dependent spouse must explain why the income is not needed to support the family, only for the dependent’s enhancement or to improve the family’s overall standard of living.  The time frame to receive approval of a work permit can be from 3-9 months, depending upon the region of the country where the relevant USCIS Service Center is located and only after the spouse has already arrived in the US in J-2 status.

The maximum number of dependents usually allowed by CHF is three: spouse and 2 children or 3 children.  If an exchange visitor is requesting four or more dependents, special procedures apply.  The teacher is not allowed four dependents during the first year.

All children must be school age.  The minimum age depends upon the youngest grade level offered by the school or by easily accessible public schools in the neighborhood.  Mothers and fathers of pre-school aged children have many responsibilities that either do not allow or discourage that participation.

Some countries approve “derivative” J-2 visas for immediate family members. If the J-2 visa holder is in correct status, s/he may apply for a work permit (EAD) only after arriving in the U.S. in order to apply for a social security number.  Form I-765 may be downloaded, fee paid by credit card and emailed directly to the Internal Revenue service.  Complete interactive Form EI-765 and submit it online:  www.uscis.gov/i-765