Once you no longer live with him then he isn't custodial (emancipation event). You should talk to a lawyer about your situation. You may be able to find free help at the Family Court or legal aid or look on Avvo for "pro bono" attorneys in your area.
If your father requires you to leave the home, and if you are not married, in the military or self supporting, you are entitled to support from your parents. You may file for support against both parents. You will ask that the money your mother pays be paid to you. You will also ask for support from your father.
If you apply for public assistance, the Dept. of Social Services in your county will file for support from your parents. The county will be entitled to the support because the county will be supporting you.
This anawer is not intended to create an attorney-client relationship and may be considered attorney advertising. This answer should not supplant advice received from any attorney the questioner may have or obtain, as that attorney will be able to provide more thorough and informed advice.