PIY - your thread/history is a true testament of addiction/abuse/denial and all the effects it has on one's life. Do not give up.
First off, the only advice I can give is from a personal standpoint. I am not a medically trained person. So here it is: Take care of yourself first. You have had a lot of trauma in life due to addiction/self inflicted abuse by your Mom/enabling this by both your sister and yourself. Time to let go and get yourself in to Therapy.
Once you have more grounding, even though you know yourself that you are not at fault for anything, only then will you be able to help your Dad, Mother and Sister. So hard to say this, but it is time for you to help yourself. Dad and Mom enable each other. Why would she stay in a marriage that involves pyscholigical and physical abuse after her kids are grown??? Why would she blame you for not being there for her??? Why is your sister denying the truth?? Get yourself removed and seek help alone.
Once YOU and only YOU can go back to your family and state the obvious, will all of this ever heal. Will it happen?? I truly doubt it. No one in your family has confronted either your Mother of Father about the obvious truth. Your Mother needs you and your Sister for support. She does not want to acknowledge and accept her own life and decisions.
You on the other hand, do not have to repeat history. You can and WILL live a happy life with or without them. It is up to you. Most of my family is dead and I miss them tremendously, but if you are being truthful in your statements, then I am happy that I had a great family and they are deceased from health reasons or addiction. YOU CAN STOP THIS PATTERN FROM REPEATING.
Be honest with Mom, Dad and Sister. State that you are going for therapy and they are welcome to attend or get their own. Do not give in. Tell your Dad the trauma of his addiction and the life he in your eyes have left you with. Tell your Mother that you do not and cannot understand why she allowed and continues to allow this behaviour towards all of the family. Is she and addict or a co-dependant??? Tell your Sister, that if she want's to be favorite and not try to get help for your parent's - it is all in her hands.
GET YOURSELF HELP FIRST. Stop this right now. You will never move on and have a healthy relationship until you resolve past issues and learn to deal with the reality of now. Save yourself. Live a happy life with or without your family.
Sorry for coming of harsh. Welcome to SR and PLEASE keep posting.