One of two things is a critical problem here.
Either you don't have a good grip on which equipment does what....OR you just aren't explaining the situation correctly.
Where exactly in Northern Florida are you ?
Do you own a multi-meter ??
You probably have two units. One makes 12 V from 120 AC. It is called a converter/charger. The other unit is an INverter. It makes 120 V AC from a 12 V input from the batteries.
Those two units have NOTHING to do with each other.
When you are plugged into shore power: The converter/charger should be making 12 V to run the lights, etc AND to charge the battery. The truck has nothing to do with that. In most configurations, the shore power is fed directly to all or most of the AC outlets and the INverter is not needed.
When you are NOT plugged into shore power, you turn on the INverter or plug it into a 12 V socket to make 120 VAC to run small appliances. THAT has noting to do with the truck either.