Ac relay under hood

You don't have a relay problem. From the shop manual: The AC compressor clutch relay is wired normally open. There is no direct electrical connection between the A/C switch or electronic automatic temperature control (EATC) module and the A/C clutch. The PCM receives a signal indicating that A/C is requested. For some applications, this message is sent through the communications network. When A/C is requested, the PCM checks other A/C related inputs that are available, such as A/C pressure switch and A/C cycling switch. If these inputs indicate A/C operation is OK, and the engine conditions are OK (coolant temperature, engine RPM, throttle position), the PCM grounds the AC compressor clutch relay output, closing the relay contacts and sending voltage to the AC compressor clutch relay. In short: those inputs are of concern, not the relay. Sure, if you provide direct power to the compressor, it works. But that's not the point. If it was, you wouldn't even need a relay. Testing is required.