In my opinion anytime the outside air is cooler than the indoor air you should take advantage of that and turn the fan from exhaust to intake and shut down the A/C (unless you want the indoor air cooled past the point of the available outside air). Additionally, I would only use it as an exhaust if the A/C had been off and the room became very hot and then only exhaust long enough to give the A/C a chance to catch up. When your A/C is running you shouldn't be using the exhaust because you are practically blowing money out of the window. I suspect that's why it seems your A/C can't keep up although without knowing room height, window size, how much southern exposure and B.T.U capacity of the unit it's not possible to tell if the unit itself is undersized.