Keep the INVERTER "off". No need for it unless you make coffee when not hooked up to shore power. Drains the batteries real fast. Keep it off. You might also check your CON-verter. My coach, two different units. Recently, found my CON-verter (13 years old) was putting out 12.4 amps.
Usable, but wearing out. (13 years old) bought a new one (Parallax 55 amp) for $209 on-line. 2 wires (+ and -) plus a copper chassis ground. Heck...even I could do that....
My generator starts with the 2 6V coach batteries. Shore power charges the coach batteries but not the 12V starter battery. The starter battery gets charged by the engine alternator...and when running, the engine alternator ALSO charges the 2 -V coach/house batteries. Go figure.
My slide-out (Powergear) works off the 2 - 6V house batteries. No matter what brand batteries I use, I seem to always need to change them around the 3 year mark. Right now, I'm using DEKA for all 3. 2nd year. So, for me, with batteries, I go for the buck when buying them...seeing any brand I buy simply lasts the same amount of time.
FWIW, my Powergear hydraulic jacks, the control panel works off the 2 - 6V batteries but the pump/motor works off the 12V battery.