It's difficult to troubleshoot electrical problems over the internet because a qualified person who is physically present will notice things going on that may not be obvious to others.
If you've replaced at least one of the batteries, chances are that the inverter/charger, the wiring, or the battery disconnect are to blame for any remaining problems. Checking voltages at each of these points with the charger operating should identify the problem. Some inverter/chargers have a variety of different modes and have to be turned on manually in addition to being connected to shore power in order to charge.