How can a minor legally leave home? 

I am a lawyer in CT and practice in this area of the law.  In most states, you are no longer required to live with your parents once your are 16 years old.  16 is generally the age of consent for contracts and sex.  If that is the law in your state, then you should be able to move out to a new home and not have to obey your mom.  I suggest however, that you try to work out the issues you have with your mom as you only have 1 mom.  I aslo suggest that you speak to a lawyer to confirm the age of consent to contracts in your state as well as the age that you are no longer subject you your parents authority.  I believe that you are old enough now, but you need to confirm this.  most lawyers will meet with you initially for free.