The compressor clutch will cycle although that seems short to me. My '97 does it from about 30-45 seconds to every couple minutes depending on the ambient air temp and my '03 seems to behave pretty much the same. It should NOT stall out the engine at idle. Sounds like the idle isn't kicking up to compensate for the extra load put on by the AC compressor and the aux electric fan.

I've had problems with belts (A/C, fan and power steering) from aftermarket suppliers slipping and squealing. Doesn't seem to matter where they came from, who installed them or how they were adjusted. I have NEVER had a problem with the factory belts. I had to replace all the brand new belts on my '03 that the Jeep dealership just installed two months ago. They were installed correctly. Both myself and the tech at the Mitsu dealership checked and readjusted them several times. That didn't stop both the A/C and power steering belt from squealing. I suggest replacing the A/C belt with one from the dealership first. Slipping belts can cause some very strange behavior. Either way, that belt needs to be replaced if it's slipping that bad. You won't ever get it to stop slipping permanently once it's glazed.

Edward