Sorry leewayne when i answered your question i didn't realise you had a partner that worked, this does make it so much more difficult. When i claimed housing benefit they paid 100% of my rent.
The only thing you can to do about your neighbour is to report them to the council and environmental health about the noise issue etc, log everything and if appropriate call the police make a log of the crime number it does take time but neighbours from hell are eventually evicted though in my experience the council just replace them with yet another problem family. Because there are few council places left there are now several housing associations i live in the south and they are called south down housing and the guiness trust here, is there the same thing in your area? It is basically the same as having a council house. The Government also insist when new houses are built a certain number are made available to low income families sorry i dont really know much about it perhaps a search on the web would throw up some results.
As i said in my post before no one seems to want to tell you what you are entitled to, it seems that unless you know about it they're not going to tell you. Don't be afraid of being a pain keep on at them it seems to me those that complain and make a nuisance of themselves get quicker results.
I really wish you and your family well as i know how terrible this can make your life, i am currently stuck with a neighbour from hell myself unfortunately as he owns his house its near impossible to do anything about it.