I'm not sure that your Intruder charges the chassis battery while on shore power. Some coaches do, while others do not. In any case, the usual means of doing that would be by closing the aux start relay under control of a battery charge controller module. If the aux relay isn't working, no charging can occur.
You also need to determine if anything in the "house" is being powered off the chassis battery. Sometimes a previous owner or a sloppy RV tech will wire some 12v circuit to the chassis 12v system rather than house, thus drawing power from it while parked and causing it to go dead sooner rather than later. One quick way to find out is to disconenct the ground cable from the chassis battery (while parked, of course) and see if something in the house part stops working. Your entry step will probably be affected and that's normal, but not much else.
Former owner of 2004 American Tradition and several other RVs
Home is West Palm Beach, FL