Been discussed in the forums many times. The only way to get the trailer wiring to work is to have it flashed by a dealer with a Chrysler Scan Tool. Nobody else can do it. $90 is the going rate. Not many dealers are going to do it for free unless you had negotiated it into your purchase price. It is basically 1 hour of shop time at many dealerships. Perhaps if you have some other work done at the same time (oil change, 15K maintenance, etc) they might cut you some slack since it actually only takes about 20-30 minutes to do the scan. Perhaps if you take it in and tell them you are having some other problems that require a scan for your build date, they will throw it in. Here is a list of TSB's:
Another reason to get the GC with the factory towing package, because by the time you get done with all the fussing around, it is going to cost you more than the $595 (2011-2013 model invoice pricing) or $795 for the 2014 V6 models.