I'd recommend to do this in stages. You will be able to assess your needs after trying it out a few times. As Pianotuna states, cheap or free campgrounds abound and pulling in every other day or at other intervals will get supplies replenished, water dumped, and afford other comforts, if needed.
The generator use sounds uncomplicated for AC comfort until you actually have to do it. Moving every 1-3 days and having to store and secure generators, carrying gas supply, and the noise will have you rethinking their use. If you plan to camp in National or State Parks, there may be restrictive use hours, also.
My suggestion would be to start researching a small solar system and upgrade of your single battery. If you travel with kids and charging/use of electronic devices, along with the sundry DC draw of trailer items, your single grp. 24 battery will not be up to the task for boondocking. In fact, one afternoon's typical use and the need for a furnace run will probably draw the battery's state of charge below 50%. Do that for a week and you will be buying a new battery. Changing incandescent lighting to LED lamps is a sure-fire way to save battery power.