Your quality of life will be much higher as a single mother of 3 looking for Mr Right, than of what the situation is now. This sounds like as bad as it gets. Anything is better than this. You will get lots of support as a single mum, housing benefit etc. If you feel guilty about this just tell yourself one day when your kids are older you will work again and pay tax - so the benefits are your right.
My ex refused to leave too and one day he got overly abusive and I snapped and rang the police. They came round and ordered that he leave the property and stay away for the night so things calm down, and luckily he left and didnt return. And that was that after months of hell it was over and I got on with my life. A year to the day later I met my mr right and are still together now over 5 years later.
Think positive and do something - you will be fine. You can find a way of being happy. And your kids will be happy knowing Mum is happy.