OP what sort of answers do you actually want here? Because IF we leave aside all the suggestions to change the situation you claim are irrelevant and impossible, There is really only one question you are asking: should I buy/rent a second property to live in?
To which the only answer surely is: if you want/need to for whatever personal reason and critically if you can afford to, by all means knock yourself out.
What is the dilemma, really, if not that the situation prompting the question is unreasonable and not sustainable?
It seems to me that you posted this with minimal information and are answering reasonable questions with such terse hostility because you WANT everyone to make suggestions that are obvious so that you can knock them back and prove (to us, to yourself?) that your situation is impossibly difficult. I can't see what one earth you are getting or were hoping to get from this thread otherwise really. What were you expecting or hoping for?
You sound very angry, very frustrated, very depressed. I think if you think your children will be fine in your house on their own, and you will be happier living in your own house/flat away from them, then there is no logical reason not to do so and it isn't even a question.
But I also think you should see your GP and talk about the toll this is all taking on you - not to get help for them as you say it won't be offered and even if it was wouldn't be accepted. But for you as you currently sound as though your life gives you no pleasure. That isn't something it is safe to just ignore, no matter how brusque and matter of fact you revel in being. Depression kills, and it creeps up on you. Take care of yourself.