COS from B2 to H4

Hi, My kid, spouse, and I came to the US in mid-June. I’m on H1, valid until 2024 and my kid and spouse are currently on B2. Now we want to join the kid in school and would like to know the best way to do it? Can we apply for COS(I-539) from B2 to H4 and join her in school while the application is pending? We tried getting the kid visa slots in India and Mexico but no luck. Any help/guidance is appreciated. TIA

You may apply for change of status after 90 days of entering on B2 however note that it may take several months to get it approved.
Check with the school you plan to admit your child. I don’t think they ask for legal status documents so your child may get admitted while the COS application is pending.

Thank you. Do you foresee any issues if we do COS before 90 days? Waiting 90 days will be too late for the school. Also, when we file 539 does that make her H4 or still B2?

While changing from B2 to other non-immigrant status may not be scrutinized as strictly as adjustment of status, it may still create issues. I would suggest hiring a lawyer to apply the COS rather than doing yourself.