I've got a separate battery bank that is dedicated to a small inverter. Runs a
laptop computer, small TV etc, when anchored out. It's a great idea, and really
extends the life of the house bank between
recharges.

But I'm in the Pacific NW. What's solar energy? :-)

If you put two battery banks on one solar charger, you'll probably need some
sort of diodes or what not to keep the battery with the lesser charge from
attempting to equalize with the more highly charged battery- a circuit might be
completed through the internal wiring of the charge unit itself. Any time two
batteries are connected to the same circuit they can't be considered isolated.