1. Plugged into shore power? No, or Yes with 30 amp, or 50 amp?
2. Aqua Hot diesel burner and thermostats are ON to provide interior heat?
3. Fridge is ON?
4. Insta-Hot at kitchen sink is ON?
5. Ceiling lights are ON? Halogen or LED?
It sounds like something electrical is turned on and the house batteries are not fully charged. If the house batteries are fully charged, then without the inverter-charger engaged, they should be showing 12.6 volts.