You are so right - hating your mother is not a solution. I once read somewhere that hating someone is like drinking poison and waiting for someone else to die. Hate does a lot more damage to you than to the person who is the object of your hate.
Your mother is showing you with her behaviour how NOT to express your emotions. Violence of any kind, whether it is verbal or physical, is not good for anyone involved.
It sounds like your mother requires help dealing with her own behaviour and you cannot give her that help. I would recommend that you talk to your General Practitioner and ask what resources are available for you and for her.
Apart from that, here is what you can do about your own stress:
Find a quiet place a few times a day where you can sit on your own and focus on your breathing. Breathe deeply in and out a few times. When you are so stressed, you forget to breathe deeply enough, and as a result you do not get enough oxygen in your body. This makes you even tenser.
While you are in this quiet place, focus on a point on the opposite wall - anything - and keep looking at that point until you feel your eyes will cross. Keep looking at that point until you feel you can no longer see anything specific, and then still keep looking at that point. You would be surprised to feel how the stress and tension flows from your body. This will help you at school as well.