Form DS-2019 (formerly known as an IAP-66) with your name on it

Sorry for late response. You need a copy of your LG's DS-2019 Form which should have your name on it as spouse. If you already mailed the I-539, just waite for the RFE if CIS needs to check it.

To work as J2, you need to apply Form I-765, Application for Employment Authorization.

Here is a link

http://www.uscis.gov/portal/site/uscis/menuitem.eb1d4c2a3e5b9ac89243c6a7543f6d1a/?vgnextoid=b69c83453d4a3210VgnVCM100000b92ca60aRCRD&vgnextchannel=b69c83453d4a3210VgnVCM100000b92ca60aRCRD