Thanks Greg, sorry for the confusion.
I will try to clarify what we have and what the issues are.
I recognize that what we currently have may not be the best.
Yes, we camp in temperatures well below freezing.
The Lithium battery is charged by the alternator while driving.
This battery powers the fridge while driving.
When camped, the fridge is running on propane.
When camped, the battery also provides 12V to the diesel air heater and diesel coolant heater.
The main issue is that I think the current lithium battery may not be suited for charging when it is below freezing. If it doesn't have enough charge, or if it dies because of improper use, I can't run the coolant heater in morning in winter, and I am stuck in a perhaps very remote area in winter.
The main house bank (AGM batteries, charged by solar) are not connected to fridge, air heater, or coolant heater. The main house bank is only for lights, and for powering 2 laptops (with inverter), cell phone booster, charging small devices when camped. It is currently only charged by solar (or 110 V shore power, but we are rarely camped where we would have access to 110V). It is working fine as is, though in winter I sometimes barely get enough charge from the solar panels and this makes me wish I could also charge the AGM batteries on the alternator. Perhaps I would need another charge controller, I don't really know.
Ideally, I would replace the AGM batteries with lithium batteries that can deal with very cold temperatures. Ideally, I would charge those new lithium batteries through solar, and also have the option to charge on alternator. But... that may be a very expensive undertaking, the main bank is not a big problem now, and the AGM batteries are only about 4 yrs old. On the other hand, I would have only 1 battery system then and be done (delete the current lithium battery, connect fridge, air heater and coolant heater to the new main bank).
So, rather than replacing the entire main bank and charge controller, my first thought is/was to make sure the current lithium battery is replaced by another lithium battery that is designed to deal with cold weather (heated battery, potentially move into the inside of the van).
Does this make sense?
Thanks for your thoughts and advice!