Not charging and the check engine is on

The first thing to do is read and record the diagnostic fault codes. Chrysler makes doing that yourself real easy. Cycle the ignition switch from "off" to "run" three times within five seconds, leave it in "run", then watch the code numbers appear in the odometer display. Here is a list of the code definitions to get you started:

https://www.2carpros.com/trouble_codes/obd2

This sounds like more than just a charging system problem, but to start the diagnosis, when the problem occurs, measure the voltages on the two smaller terminals on the back of the alternator, and on the larger bolted-on output wire. Those measurements must be taken with the engine running.