@EnviroProf my T250 was ordered with HD alternator (250A) and dual AGM batteries. I connected the 2000W pure sine inverter to the dual batteries and house battery with the use of a manual select switch (off, van or house). I went inverter only (Samlex $576) with seperate 50A shore charger (Samlex $333), and transfer switch (WFCO $67) for maximum control with only a bit more wiring. An all-in-one inverter cannot invert and charge at the same time to my knowledge. My system can. Also, if my transfer switch or shore charger goes bad, I only have to replace that component, not the entire all-in-one inverter charger.
The alternator can power the inverter while idling or driving. That way I can charge house battery or run rooftop AC anytime I wanted too.
I can also charge house battery or run rooftop AC off of shore power or generator.
I can and do run inverter off of house battery for TV, and coffee as needed. If I really had to, I could run roof AC off house battery for a couple of hours although I'd rather idle the quiet van engine. That is where SEIC comes in. I can select idle anywhere from 900-1800 rpm for higher voltage and lower amps. The van battery stays fully charged doing this.