It sounds your situation is much like mine, the only difference being that my mother doesn't use alcohol: She's a manipulative bitch even when sober.
Okay, I started from the middle. I turn twenty on 26Th of this month and I have cerebral palsy, causing me to be unable to walk properly and without support. For eighteen years my mother was abusive both physically and mentally. She called me names, kicked, slapped and shoved me around and all in all made sure I understood that I would never accomplish anything and I overall sucked as a human being. I too loved her, afterall, she is my mom and I am supposed to love her. I blamed myself every time she got mad, I thought it was my fault. Almost every fight started because I couldn't do an exercise she wanted me to do (she had devised these exercises herself and she has no education to qualify her to that) or I didn't sit straight. Yeah, shocking. I never knew that not sitting straight would deny me a place to study, a job and overall happiness in life. *rolleyes*
But like I said, at the time I thought it was my fault, that everything was my fault. Then finally I had enough. My mom and my dad had had a divorce with me at a very young age, and I visited my dad every other weekend. One of the usual morning fights broke out on Friday morning and I left to school with my mom waving the finger at me through the window of the taxi. The fight continued as I got back home and didn't settle before I left for my dad, so I decided to not come back. I was lucky. If the fight happened on Thursday, I would have lacked the courage to not go back. I would have again thought that it was my fault, that I'm a bad son who causes stress for his mom and I had no right to complain.
After living with my dad's new family for two years now, I've figured out that all the hardships were not my fault. My mother excelled at dodging responsibility. When he tossed my phone across the house, shattering it to pieces, she didn't think she had done anything wrong. Every time she kicked or slapped me, she didn't think she hadn't done anything wrong. She knew how to manipulate me into thinking the same, heck, she almost got me to not press charges on assault against her.
After this lengthy explanation, I hope you can understand the next words better. You shouldn't feel responsible of your mother. You shouldn't be worrying of what happens to her if you leave. You have enough problems as it is. You shouldn't feel that because she's your mother you should forgive him, or take the bullshit she throws your way. Same goes for your grandma. There's a limit you should tolerate even from a sick person, and since she clearly has chosen her side, consciously or not, you should take a firm stand on your own.
You are an adult and no one has the right to call you names or talk to you like you were an idiot. You've tried to help them both, you've tried to make them see and that is as far as you can and should go. Leave, and don't feel guilty. Out of my past experience, that is precisely what your mother wants. He wants you to feel guilty so you keep coming back and she can make herself feel better by being an asshole towards you. Make no mistake, mothers are experts at mindfucking their children and will not hesitate on using that skill.
Not everyone should be a parent, being a parent does not absolve one of all the bullshit one brings to this world, and when a person is like that, her being your mother is no excuse. Leave and live your own life. You have no responsibility over your mother.