Car jerks when you shift to drive? No lights on…what is the problem?

Well, the variable here is that you just had the rear differential replaced. What about universal joints? What about something to do with the repairs performed? If you have had three dealerships evaluate the concern, I'm not sure how much I could suggest otherwise. Unless they were not able to duplicate it. The key is to duplicate the concern in the workshop environment. Perhaps that's what's needed?