That "huge chassis battery" is the one that starts your engine.
You probably need at least one chassis 12v battery that provides about 1,000 cca (cold cranking amps) to start your engine.
The smaller 12v deep cycle battery might start your generator (mine does). One typically finds these batteries on boats where double duty is required due to space limitations. These are not designed to start a large diesel engine.
When not driving, turn the chassis battery switch off (my switch is in the battery compartment.) Only the generator and the alternator recharge the engine battery in many rigs. Then when you have time, start chasing the cause of your chassis battery drain.
Shore power likely does not charge the chassis battery on your rig unless gadgets (like the trik-l-start) are added to your system.