Good afternoon and welcome to JustAnswer!!!
It sounds like the shop was trying on parts and not doing any diagnostic work to determine the cause of the no charging issue.. I have attached the wiring diagram for your 2009 Ram W/4.7 engine.. I don't know what's wrong with it but I will help you test to determine what's going on.. Here is a breakdown on how the charging system works.
The charging system is turned on and off with the Powertrain Control Module (PCM) and ignition switch with engine running. The field circuit will not be energized until engine is running and ignition switch on. This voltage is connected through the PCM and supplied to one of the generator field terminals (Gen. Source B+) at the back of the generator. The generator is internally grounded. The generator regulates the field using pin-1 of the field connector (high side driver).
The generator is driven by the engine through a serpentine belt and pulley, or a decoupler pulley arrangement.
The PCM receives a voltage input from the generator and also a battery voltage input from the Totally Integrated Power Module (TIPM ), it then compares the voltages to the desired voltage programed in the Electronic Voltage Regulator (EVR) software, and, if there is a difference it sends a signal to the generator EVR circuit to increase or decrease output. It uses a Pulse Width Modulation (PWM) to send signals to the generator circuitry to control the amount of output from the generator. The amount of DC current produced by the generator is controlled by the EVR circuitry contained within the PCM.
Voltage is monitored at the B+ terminal stud to insure it is connected. If the B+ cable is loose, the PCM will shut down generator field. Because of this new feature, pin-2 of the field connector is internally connected to the B+ terminal
The first thing you need to do is make sure you only test when it's NOT charging, if you test when it's charging you will not find the cause... When it's not charging I need for you to grab a multimeter and see if the Red/Gray has 12v on it and then check the Brown/Gray for a ground. Now to test ground you will need to clip the multimeter or test light to positive and then probe it.. Fuse 33 is the output and it should have charging voltage around 13-14v as well as the big B+ wire at the back of the alternator..
Depending on what's missing you will need to follow the wiring diagram to find the cause of your issues..
I hope this helps, and if you need anymore assistance feel free to give me a reply..
Thank you for the positive rating and have a great weekend,