First it is a Hymer Sunlight Van One with lithium battery and underhood generator which is actually a second alternator. The AC is a typical RV AC unit and the wiring is designed to run off the lithium battery alone for a short period of time or with the engine/generator running or shore power. That is the reason it is wired thru the inverter/charger. It is an interesting setup that has problems with the setup for many.
I posted simply to alert the OP that my experience was challenging since the OP stated he had an inverter/charger also. Mine is all fixed now thanks to Beaver Motors in Beaver Springs PA.
I did post in the Class B section about my issues several months ago. I also posted in the facebook group under Carado/Hymer owners. I certainly was not interested in hijacking this thread.