Assuming the kids are getting home schooled.
We heat with wood. I've lived with a well previously, as many country people do (I miss it here--city water chemicals taste terrible.) Plenty of people have composting toilets. If the dad is a chef, they're probably eating pretty well, other than those poison shrooms.
The people that bought the land next to ours were living in tents, before they finally brought in a couple old campers. No running water. A generator for electricity. Trash and garbage everywhere. I went in and talked to the county people. They said there's nothing you can do about it because they are, "camping," on their own land. They did finally clean up some of the trash a few weeks ago. Mr. Bayard has been talking to the guy some while he's putting up our fence posts. We hadn't fenced that field previously, but are now. One of their pitbulls came charging out at my horse and I last month, and he jigged, when I jagged. Broken ribs, when I haven't come off a horse in 40 years. But....I digress.
It doesn't sound like these kids are being abused any more than Appalachian or Native reservation kids in this country.