2 years is a very brief period of time in the scope of your life. You are dealing with an abusive, angry alcoholic. And it will get worse as the disease progresses...which it will. You have children to protect, that's a deal breaker for me. The lease is a very small problem compared to the life you are exposing your children to. Talk to a lawyer, or talk to your landlord even. Find Alanon and get help for yourself.
You have to get out of this before he turns that inability to control his anger on your children.