"with guaranteed wage, contract and German NI equiv all paid."
Presumably that includes health insurance for you and your DS? Non-earning dependents under (I think) 25 are included with a parent's insurance free of charge, as long as you're with a public insurance agency not a private one.
"DS16 would have to give up his college course and come with me."
frosch makes an important point. 16 is a tough point to change if he doesn't have any German. Is he currently doing A-levels at college or something more practical? A small town won't have any educational provision for English speakers, a major city might have only private schools in English, and places like Berlin do have quite a few options, but it's really difficult with no German at all. I know of one or two private schools in Berlin for ex-pats that offer A-levels, but they're very expensive, and a state school that offers the international bac, but it has waiting lists a mile long. The problem at 16 is that the state no longer has an obligation to educate him, so they're not going to be too bothered about his language skills. If he wants to do an apprenticeship he'd have to brush up his German first, surely.
frosch is also right about the differences between different parts of the country. If you live in Munich your expenses will be huge by comparison with Eisenhüttenstadt (look it up). But there's no way on earth I'd turn up in Eisenhüttenstadt, however cheap it may be, especially with a teenager in tow.
What exactly what do you want to know from us? In all honesty, you sound like you have zero interest in actually going and living in Germany, but you'd do it simply to get out of the situation you're in right now in the UK. I think that kind of attitude is almost certainly often doomed to failure; if you come to Germany (or anywhere really) it needs to be because you can genuinely see yourself integrating into the society and benefiting from the culture, rather than being a last ditch solution.
I taught English when I first came to Germany, but that was nearly 25 years ago and I was childless then. It's genuinely enjoyable and almost everyone I taught, from young to old, were lovely and enthusiastic people. DH still teaches, but at university level. It's relatively rare to get a proper contract, most people are freelance, so that's a good indication for you from the start.