If that is true then there is some very large parasitic drain on the house battery while driving.
Also if it is getting a charge, then running the inverter shouldn't be as much of an issue as it has been for us. After a few hours of running the TV on the inverter, it starts to yap about low voltage. Something is not right...
Carl & Dawn
2015 Greyhawk 31FS
2015 Ford Transit Connect (our TOAD on a DEMCO Dolly)
DW, DSx2, DDx2 Catx2 Dog
Tampa Bay Area of FL