'02 Santa Fe - Dealer is perplexed

About a month ago my '02 Santa Fe's dashboard battery and parking brake light came on while driving. When I stopped the vehicle numerous lights(ABS, TCS,
etc.) joined the others. As I kept my foot on the brake and gave the engine some gas ALL lights went off. I drove the car the rest of the day without problems.
Last week the battery and parking brake light came on again, yet near the end of my trip approximately 8 miles, the RPM reduced to ZERO. Luckily I had parked and the car cut off. I left the car for nearly 3 hours. When I returned the vehicle started without hesitation and no lights lit on the dash. A few miles down the road, I applied the brakes, the car jerked forward to a stop. I managed to back it in to a parking space (did not jerk when brakes applied), still no RPMs and the car cut off.
Roadside assistance was called and I received a 'jump' and began to pull out the parking lot. The vehicle began jerking with braking, no RPMS and all lights of the dashboard came on. I then called roadside assistance again and the dealer---vehicle was flatbedded to dealer.
The battery was replaced about 18 months ago, so I suspected it was the alternator. When the vehicle was dropped at the dealer, it started instantly with no problems. After keeping the car over night, the dealer could not find anything wrong with it. Yet, due to nature of the full complaint they kept it until Monday.
On Monday after driving the vehicle for nearer the entire day----the problems began and they replaced the alternator and the recall item---serpentine belt. The alternator was done on warranty. The dealer's explanation was when the car got hot, the problems began with the alternator.
I have noticed the vehicle is running near half way mark of the temperature gauge. This is not usual for this car. Further the RPMs when idling is less than 1.
Presently, all the conditions began Friday before last, began last Friday (5.19). I just had the vehicle flat bedded to the dealer again.
Does anyone have an idea on what is causing the problem(s)?
--
OnTheWay2Dissappointment

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Sounds like your problems are fixed. It's a frequent occurrence for Hyundai alternators to work properly when cold and then fail to charge when hot. An faulty alternator would cause all the problems you describe prior to the alternator replacement.
It's normal for your car to be running at halfway on the temp gauge and the idle speed to be below 1000 RPM.
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