I have replaced many of these for lighting issues but that was the lights on the truck only not on a trailer. I have never heard of resetting the module before.
On Dodge trucks I believe 2006 and up there is no fuses for the trailer connector, it's all computer controlled. If you have a short it will kill the circuit on the system and you will have to go to the dealer to have it reset. After I believe 4 times it got reset you will have to replace the module.
Stupid system ? YES, very !!! You can bypass it, but you need to build a separate electrical system with relays, and requires a little expertise on this.