As long as your B1/B2 is still valid (you are within the timeframe on your I94 and you didn't invalidate it by working or studying), you should be able to file a 'change of status' request. I believe you have to submit a copy of your wifes DS2019 including the second page that carries your name and a copy of your current I94, B1/B2 visa and passport demographic page. USCIS sends you a new I94 with the new expiration date (or more likely one saying J2 D/S). This way you can avoid the trip home. You would have just the new I94 and the B1/B2 visa, you would never actually get a J2 visa stamp in your passport. Be sure not to file this request too early or too late. If you file early, they could deny it saying that you came to the US with the intent to stay not as visitor but rather as exchange student spouse. If you file late, you won't get it approved in time to remain in status.