Hi there, and WELCOME to SR. This is a wonderful place to find support. I hope you keep coming back.
With regards to your ABF (alcoholic boyfriend), is he on the lease? If so, you may need to figure out if HE needs to leave of if YOU and your child will. If he isn't, then you are within your rights to ask him to leave. I suggest discussing the matter with your landlord.
I went through something similar when my XAH (ex alcoholic hubby) and I separated. We had signed a lease together so we were both bound by law to stay until the lease was expired OR find a replacement tenant. Instead, we had the lease transfered to XAH, who signed off on the document, claiming that he would now be in charge of the entire lease. I had my superintendant sign off on this and had to send the documents to the landlord via registered letter. That way, I'm protected against the landlord coming back and asking me to pay whatever rent my XAH defaulted on (they have up to 3 years after the end of the lease!). In the end, it's a good thing I did this because XAH did end up defaulting on the rent and pulling a midnight move on the super...
I applaud you for putting your sanity and your child before your boyfriend.
Keep posting!!