Seeing as your children are teens and you've gone on about how much you hate them and they hate you... why not let them get a job themselves and pay for their own activities. There's teens, there is nothing wrong with expecting them to pay for their leisure activities. If you can't provide the basics then you shouldn't pay for luxuries - and you can't pay for accommodations.

You can also find somewhere with a roommate. Or yes, live in a "bad area". How is that bad area going to be worse than living in a home that you hate living in? You would have privacy and you would be away from all the hate that you use your energy on. It sounds like a win to me.