First off a week is pretty fast for the batteries to go low unless they are old enough to be marginal, otherwise you need to look for what is draining them.
As for chassis battery charging I am going to add it because I want my solar to keep my chassis and house bank topped off.
This is the unit I am looking at now. ME-SBC
My solar charges have a trickle feature but I want something that that has a flexible stop and start setting so I don't unnecessarily heat my chassis batteries.
I'm not sure I would get one if I didn't have solar because
1. The inverter/charges them from grid power.
2. If I don't have a power source like solar or grid I don't see why would drain my house batteries to keep my chassis up.