You're right to be concerned it's going to let you sit. The mistake that was made is the charging system is failing intermittently and that's when any testing has to be done. If it's tested while the problem isn't occurring, of course it's going to test okay.
The most common cause of intermittent operation of the generator on any brand of car is worn internal brushes. Those are real easy to replace on most Chrysler products, often without removing the alternator from the engine. Ford went to a similar, real nice design in the '90s, but by 2000 the engineers figured out it was too easy to diagnose and repair so they buried the voltage regulator and test points, and made servicing the unit very difficult. On the older ones there were two key test points right on the back. One was even labeled as such. Those made it real easy to determine if you needed a voltage regulator, brushes, or if it was more serious.
Output of the generator is not monitored by the Engine Computer, so it's not going to have a diagnostic fault code telling you what's wrong like they do on Chryslers. The only thing it could potentially set is a code related to low system voltage, but you already know that from the warning light and the "Volts" gauge on the dash. Low voltage adversely affects the many computers on the car making them do weird and intermittent things, so don't concern yourself yet with the engine running problem unless it continues after the generator is replaced. Worn brushes can continue to work on and off for weeks or months, but they will stop working for longer and longer periods of time as they continue to wear down and make intermittent contact. The car will be running on just the battery, and with the head lights and heater fan off, that won't last much over an hour before the engine stalls.
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Monday, January 6th, 2014 AT 3:46 PM