Problem with A/C and heat

My car is the Touring 2.4 automatic non turbo model. So when the car is parked or at idle, with either the A/C running or the heat at any speed, I am guessing the compressor is kicking in, the rpm's drop, the car shakes like it is about to stall then returns to normal. Happens about every ten to thirty seconds.

With the A/C after it happens a few times the air will start getting hotter and hotter until it just blows warm air.

i tried adding refrigerant but the gauge read green before I added it. I am guessing the previous owner had topped it off once or several times without bleeding the system. Would that cause the compressor to kick on more often/harder than it should?

I have a vacuum pump for A/C systems so I could do it myself? I just want some expert advice of other things I should check before I waste several hours checking things that do not need checked. I am good at fixing but not diagnosing.

Thanks