Remote Control Door Lock Receiver (RCDLR)
The remote control door lock receiver (RCDLR) is a multifunction module that operates both the keyless entry system as well as the tire pressure monitoring (TPM) system. When an RF message is received from a keyless entry transmitter, the RCDLR interprets this signal and will request via serial data that the body control module (BCM) perform the specific function, i.e. door lock, door unlock, or vehicle locate. The RCDLR also sends messages out to the 2 Way Advanced Remote Start transmitter.
Remote Control Door Lock Receiver (RCDLR) (AP3 or AP8, without E52)
Top rear of the passenger compartment above the rear window
Remote Control Door Lock Receiver (RCDLR) (AP3 or AP8, with E52)
Left rear of the vehicle behind the D-pillar trim panel
Body Control Module (BCM)
On the lower left side of the I/P to the left of the steering column
There are a lot of things to check. The idler is not the same as the tensioner, make sure they are both ok. The compressor could be experiencing lockups from contamination or ice build up / fluid entry due to charging or condenser problems. A used belt is a used belt, they stretch, even after 5 minutes. Make sure the belt size is correct.
You need to run an OBD2 fault code test on this, it is the most important test you can do in order to make sense of what is going on. The test can be done by any Autozone parts store for free or other store like them.