The only thing that happens when adding a second battery is you may not have enough AMPS coming out of the converter/charger to handle two batteries. A typical rule of thumb for maintaining two 12VDC batteries you need to produce around 17-20AMPS DC Current for each battery in the bank. Your in-line fuse close to the battery bank should be a larger value than the rated DC output of your converter/charged unit.
If battery draws requires more current from your converter/charger then it is rated for it will just simply blow the fuse or trip a breaker etc...
You should have two REVERSE POLARITY FUSES on or near the converter/charger unit and there should be an in-line or perhaps a breaker mounted real close to the battery terminals to protect the wiring from burning up with excessive DC current in the setup.
Looks for those fuse points before giving up on the converter/charger unit. the best test is get a DC VOLTMETER across the battery terminals. Without shore power or generator on you should read 12.6-7 VDC if your battery is near 100% charge state. Then turn on shore power and the DC VOLTAGE should jump up to 13.6VDC or whatever smart mode the charger is doing across the battery terminals. If you don't see the jump in DC voltage then the fuses may have blown or the converter/charger has failed.
The next test is to then go the the DC OUTPUT leads of the converter/charger and measure there for the 13.6VDC when shore power or generator is on. If you find the 13.6VDC there then the converter/charge is good. You also have to check the 120VAC input line to the converter/charger. My unit has its own 120VAC Circuit breaker in the power distribution panel. This may be tripped as well if you don't see the 13.6VDC output voltage...
Sometimes the batteries will boil out their fluids and this will result in an shorted cell and when sore power is on the converter/charger will see this short out and blow the fuses etc...
The PD series converter/chargers are very good units to have... I have got great use from my PD9260C 60AMP setup for my larger battery bank...
Roy Ken