Not clear where things stand with that 12.3 after driving a little.
Do you have any alternator charging or not? If not, you might not get any charging from the converter by running the gen either. Although you might still get gen charging if no alternator charging. Have you tried that?
Your batteries do need recharging for sure, so you need to know what you have going there before they die while you are still away camping.
You can take the house batteries home to charge them up after camping trips, and keep them on a trickle charger/maintainer, and use your little solar panel to maintain the engine battery--but you have to make the solar do that if it does not now.
Here is some good reading --it helped me a lot!
http://www.bestconverter.com/Books_c_67.html