Don't confuse an INVERTER with a CONVERTER!
The former transforms 12V DC to 110V AC
The latter transforms 110V AC to 12V DC with sufficient capacity to charge your battery(ies) AND power all the 12V appliances in your unit.
You need to find your CONVERTER and check to make sure it is providing those 12V. If it is working properly it will charge your batteries just fine.
You probably do not have an inverter.
The other thing you need to check is the drain on the batteries when you are dry camping.
Fridge, CO detector, propane detector all draw a small current even if you are using nothing else.
Add a few lights, water pump and the furnace fan and you will not make it through the night on a single charge.