I agree with Beau on putting the USE/STORE switch in USE if the coach is plugged in.
I'm not so sure the chassis battery isn't supposed to charge when plugged in regardless of the position of the USE/STORE switch as that switch (relay) just disconnects the house batteries from the DC buss. If the voltage on the DC buss is high enough above the chassis battery voltage, shouldn't the cross-connect engage and charge the chassis battery?
I'd be looking at that cross-connect relay. Start by engaging the emergency start switch and see if it switches position.
Ted & Melinda
2016 ACE 27.1
2016 Chevy Sonic Toad
2020 Chevy Colorado Z71 Trail Runner Alternate Toad