Dodge vans started putting the VR in the engine computer in 1988 for the 318 and 89 for the 360 engine.
Voltage seen will be influenced by electrical load on the system and what the ECM's VR allows.
Running the absorption fridge on DC, along with blower motor on high, at idle, is simply more than the alternator can make even fully fielded.
When my alternator was failing, with what mex said was a shorted stator, it was able to produce less and less, requiring more rpm to maintain voltages above 13.0v.
Failure of the VR in the ECM either requires a new ECM, or for one to bypass it and wire up an external VR.
The 10 ohm 50 watt resistor needs to go in between former field wire terminal connector to alternator to keep check engine light off.
https://alternatorparts.com/external-voltage-regulator-high-output-alternator-kit.html
I basically used the above link, but instead of using the Mopar VR, I used the Transpo540HD for a Ford, which had the internal potentiometer to adjust voltage. I just modified the VR to accept wires for a remotely mounted VR.
This superior Modification was possible for me due to Mex's knowledge and helpful nature.
Now if the alternator can not raise battery voltage to above 13.7v ever, even at higher rpms then I would say the Alternator or VR is failed/failing, but at idle when maxed out and the voltage can't be held above 13.7v, that is to be expected simply because of lack of RPM.
If the loads are higher than what the Alternator can produce, voltage is going to fall no matter what the VR is asking for.
I also have a K type thermocouple epoxied to the additionsl heatsink epoxied to my transpo VR. At Idle with a big load the VR temperature also climbs as the field current maxes out trying to maintain the voltage I have chosen. More RPM has VR temperatures decline again, and My VR is inside my Van, not in engine compartment and engine heat or underhood airflow are not influencing variables.