Water will be more of a limiting factor than battery power. With 4 people taking showers and 30-40 gals and your first time dry camping you will be hard pressed to last 4 days. I would start at NF CG's first and see how you do, most have water that you can get to fill your 10 gal container. The other thing to look at is do you have enough gray and black water capacity to allow you to stay longer with a water source. If you have 2 6v Golf Cart batteries they should last you 7 days with with minimal usage(water pump,refer, WH, no TV or X Box). I would camp in higher elevations so you don't need AC. Also plan on stopping once a week at a FHU CG to recharge your batteries, refill your FW and recharge your batteries. Once you and your wife determine that you like this type of camping then I would look at generators or solar but your water issue has to be dealt with first.