Well, I don't think student housing would work out all that well. I'm probably still not at a point where I could take care of myself if I were out on my own.
Hell, I still need help doing laundry. Though hopefully I won't have to keep bugging others now that my step-mother helped by circling the proper settings on the machines with a marker.
I understand that breaking off and doing all of the things yourself can be a scary prospect, but again, a lot of people don't know how to take care of themselves properly before they move away from home. You learn how to do those things like laundry and cleaning and so forth by having to have to do them. It's okay to screw up when you first live on your own. Screwing up is just first-hand learning of what not to do.
And frankly, do you really think your mum will respond well to you trying to become more independent at home? She seems like somebody who really,
really wants to convince you that you are codependent on her to be able to function. In reality, you don't. You're just as bright and able-bodied as anybody else, and you deserve a better life than what you're currently having. You move out, then you get the skill. When we humans suffer from people trying to put us down and rid us of our self worth, we often become unsure of ourselves, like we lack proper, firm ground to stand on. Often we become very insecure. When people are insecure, they become hesitant to find new ground - they feel as if they are ships not just without a goal but without a port to even set sail
from - and they become placated by the comfort of daily rut. They feel like at least they know what they have, even if what they have sucks, and that is better than braving the unknown. But that is an illusion, a lie made up by your brain in order to be able to endure the abuse.
Go to your university and ask for housing. Go to your father and ask for room. You know in your heart that you cannot stay where you are know, and these are your best options to get out. Go for them.