Only take legal advice from a real lawyer not the internet. With that out of the way...

On immigration.com I see:

"H-4 dependents may undertake studies while remaining in the H-4 category, however, they may not engage in any form of employment."

on Cato.org:

"H‑4 employment authorization documents (EADs) allow certain H‑4 spouses to work legally in the United States. H‑4 spouses are only eligible if their H‑1B spouses are going through the process to obtain permanent residence."

Hopefully that gives you some talking points you might take to an immigration attorney.