Hello from Oregon,
Do you actually have an Inverter/charger or a converter charger?
Makes a difference. First things first. You need to get your nomenclature correct. Then you need to take all of the batteries out, charge them and have them all load tested. If any are bad replace them first. By hot water pump I assume you are referring to the on board water pump? The rest is really confusing.
Don and Lorri
2007 Dodge 3500 dually