Given the situation as you described it, physical abuse considered, I support you in wanting to go it on your own financially. I think if you apologize, even if it is just to get the college money, you are feeding into a cycle that will allow your parents to withhold college money again in the future. With loans, yes you will be in debt but as long as you stay in good standing with your university no one can take that money away. If it will be your first time with loans, make sure you understand what those conditions are, usually it entails taking a certain number of credits per semester, and keeping a certain grade average (C or better, probably). It sounds like you will not have trouble meeting those expectations.
Good luck and keep focused on your personal goals.