Both my wife and I have J-1 visas. However, her J-1 [IAP-66] does not have the § 212(e) home country residence requirement. Why? Does this mean we can change status without having to go back home?

I have a strong feeling that the notation on the IAP-66 may be an error. Please note that it is not binding on an USCIS inspector or examiner, or consular officer. They could still look at the underlying facts and find your spouse subject to the 2-year requirement.