Instead of bringing cold air into the tent from the vent in the room that is already too hot, is there any way you can extend the intake duct into one of the rooms that is "freezing"? This might help balance out the temperatures in the apt a little more. Having the exhaust fan on in the grow room will defeat the purpose of the a/c, you would be better off with the window shut and the apt sealed when a/c is in use (or when outside temps are higher than the target indoor temp) unless you are venting directly from the tent to outside like mimedgrower mentioned. Also, if there is an a/c return vent in that room is it unobstructed? Running a separate duct from the top of the tent directly to the return vent would also help the a/c deal with the heat in that room.
This should free up the electricity and outlet you were using for the exhaust fan as well as save you some money by hopefully making your a/c more efficient.