Go talk to your father about what is happening, since he is your pother parent.
It's important that YOU take responsibility for *your* behavioral problems. Yes, your mother may say things to you that you don't like- perhaps there is a reason for that. But you and only you are responsible for the way you behave. Take control of that now. No excuses.
Here is a hotline where they can help you work through this:
http://www.boystown.org/hotline/Pages/default.aspx
Your mother has more to deal with than your issues in her life, I'm certain.
Take responsibility for working on your school work, find a tutor if you need one, and go to the library if you need to study away from home. There is no reason to move out - just go to the library if you have work to do.
Make sure you set aside time to do your own laundry, make sure not to leave stuff around the house. Don't bring dirty dishes into the kitchen and dump them in the sink- if you do your part, she will ease up on you. You say you aren't "old enough" to be emancipated- but you ARE old enough to take on the responsibility for your own stuff. Say nothing, and keep your stuff clean, andyour mother will be a little happier.
Moving in with your father isn't going to be the answer- at your age, whomever you live with is going to be your latest aggravation. Keep quiet and clean up after yourself, go out to study elsewhere, and you should be fine. That's all stuff YOU can do, if you so choose.