The issue is the visa was granted under the incorrect pretense and perhaps the parties may be getting charges of misrepresentation. The parties should have just used the spouse visa process.
Actually both couples must be unmarried at the time the petition is filed and remain unmarried until the US entry. The visa should have not been granted.
How many times have you met in person? What was the purpose of the visit? If the intent was to marry and adjust status before US entry, it's considered fraud.
Hopefully you filed for the employment authorization card and requested SS card. With that you can apply for dl or state ID. Until then you would have to use foreign passport.
I think you need appointment for SSN office. Also my wife waited a week after arriving and the clerk couldn't verify her information in the save system. She tried a month after arriving and she was able to be helped. This was last fall as a data point.