Your choice, of course.
I found out with my previous PUP that battery capacity was by far the limiting factor on dry camping (no hookups). Dual propane tanks are nice, but just one tank will outlast a dual battery install every time (at least for us).
If I were in your shoes, I would not bother with carrying a second battery in the tow vehicle. I would instead carry a small generator - 500 - 1000 watts - to recharge the single battery as needed. The A-frames mount 30 amp (360 watt) converters, and a standard size 24 battery shouldn't recharged at more than 20 amps anyway. So a small, compact, generator (I like to add quiet) will easily take care of recharging the battery without taking much more space or weight than a spare battery in the tow vehicle. And the generator will be easier to use than swapping out batteries. A bigger, heavier generator (2000+ watt for an FR A-frame with Cool Cat) will run the air conditioning OR the microwave, too.
keeping it simple so we camp more often
2014 Rockwood A122
2008 Hyundai Entourage (minivan)
camping Colorado and adjacent states one weekend at a time