I don't want to sound harsh, but I'm afraid what I have to say will. Keep in mind that I've spent the last 24 years dealing with my mom's 'issues'. Through years of therapy and soul searching I had to put my kids and family first.
One thing you can try is an intervention. There are people out there who will help you plan one and get through it. I would recommend having a counselor there to 'run' the intervention. With the intervention there will have to be an ultimatum, though. You may have to tell your mom that if she doesn't seek help and change her ways and boyfriend, she will no longer be able to see you or your daughters. I spent way too many years putting my mother's problems before my kids and finally put a stop to it. I know it sounds extreme and it really is, but the situation was extremely unhealthy for everyone. I can't change my mom, but I sure as heck can protect my kids from things they shouldn't be witness to.
I really sympathize with what you're going through. I wish there was an easy way to deal with the situation, but I just don't know of one.
I wish you the best of luck and you, your daughters and mother are in my prayers!