The voltage regulator is on the back of the alternator, it regulates the 'charging voltage' and sits around 14.1VDC. Testing is easy, connect a multimeter to your cigar lighter or buy a plug in volt meter off amazon and test whilst driving, with the engine ON you should get 14.1 VDC regardless of current consumption i.e try turning your lights on you'll see a 0.1 to 0.3 VDC dip for a sec then revert back to 14.1 VDC as the regulator does its thing. Try adding load on the car such as the rear window heater and heated seats, the regulator should maintain the 14.1 VDC. With the car off check the voltage it should be at least 12.3V anything around 11.5VDC is very low.
The AUX battery is the rear one, not the front that starts the car. If the rear battery is NOT a genuine Mercedes battery they can give issues, when replacing get the genuine Mercedes battery made by Varta, the car will thank you for it, aftermarket batteries just do not have the same longevity. Also check your BCM - Battery Control Module above the battery behind the lining, they can burn out.