Tony/Barb,
First off, how long have you had the coach? If a long time, has this problem presented itself prior to now? If you've not had the problem before and, this is a new problem, then, something is malfunctioning and, there's no need to ADD any auxiliary charging system to your chassis batteries. You simply need to repair something that's gone bad.
But, if you've not had this coach for long, and you just noticed this problem then, you need to learn about your charging system(s). This is not meant to be derogatory, just making a suggestion. Just about every coach made for decades, when the engine is running, will charge both chassis and house batteries. Different manufacturers, do it in different ways.
But many manufacturers have failed in the past, and, even some presently, to setup a charging system for the chassis batteries while on shore power. Winnebago and Itasca did just this up until around, late '05. In the '06 and later versions, a "Trik-L-Start" system was installed at the factory to keep the chassis batteries topped off while on shore power.
So, if you study your system(s) and find you have absolutely no chassis battery charging system in place while on shore power, then that's when you need to look into the many that are available. I've read of a newer, more modern replacement for the Trik-L-Start called the "Amp-L-Start". I think that's what it's called. It's supposed to be better than the previous version. Since I was not aware of any of those when I did mine, I simply bought a Napa, three stage charger and permanently mounted it inside the coach in a hide-a-way spot and hard wired it directly to the 110VAC circuit breaker panel and, then hard wired the 12VDC output side to the positive and negative terminals.
Now, my chassis battery charging system is completely separate from the Inverter/charger charging system of the coach batteries. Not that it needs to be, I just wanted it that way.
Also, one of the things you may need to look into is, is there a possibility of short somewhere in the chassis battery system that's drawing them down while being parked for extended periods of time? Again, just a suggestion.
Scott
Scott and Karla SDFD RETIRED2004 Itasca Horizon, 36GD Slate Blue 330 CAT
2011 GMC Sierra 1500 Ext Cab 4x4 Toad
2008 Caliente Red LVL II GL 1800 Goldwing KI60ND