Not sure about your coach but it's been my experience that many MH's have a split bus bar in the electrical circuit breaker box. In other words, a portion of the bus bar draws it's electricity from the inverter and only supplies certain circuits with power. When you plug in to shore power or use the generator, a gate trips within the inverter and allows shore power to travel to both sides of the "hot" bus bar. Take apart your panel and look for a split in the bus bar, if you find it, you could take a piece of 6 gauge wire and jump the bus bar thus allowing inverter power to travel to those circuity not previously energized by the inverter. When you plug into shore power it will automatically supply shore power to both bus bars and when you're on inverter power it will supply all the circuits. The only draw back is the A/C in that it will try to draw power from the inverter when you're not connected to shore power. To eliminate that possibility just make sure the A/C's are turned off when on inverter power.
2016 Newmar Dutch Star 4369
Newmar Owners Club
USAF 1966-1969,- Law Enforcement 1969 - 2003, Unemployed (retired) since March 2003