Your next biggest issue while boondocking after fresh water and dirty water management is power.
I was a bit knocked back when you said you were going to put in a couple of "decent" batteries, "but not Trojans."
We boondock a LOT and I have two OEM Deka DC-24 batteries and when they go a pair of Trojans are going in those holes.
That will give me 260AH capacity for about 400 bucks. What do you have against Trojans?
With your brood you will be needing plenty of battery supplied AC so you will also need a fair sized (1500 Watt range) pure sine inverter to keep up with the kid's electronics.
Like Caper said you will also need a good sized generator to keep the batteries charged. If you want to run the Air (you did not say what size you have) you will need about 2400 watts generator power.
There are some mods you can do to the air conditioner to make a 13.5K air conditioner work with a Honda 2000. If you have a 15K only a 2400 watt unit or up will most likely work well for you.
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW