Hi Pretzel and welcome to SR!
I am sorry that you and your family are going through this. You have come to a great on-line resource for families of alcoholics. There are some other members here that have grown up in homes with active alcoholism. We also have a forum here for Adult Children of Alcoholics. The effects of growing up in a home with active alcoholism can manifest themselves in future relationships.
I hope that you and your family will check out meetings through Alateen and Alanon. Therapy and counseling are also a good place to find help. If you are a student, you may be able to find support through your guidance counselor.
Your mother may not be telling the truth about AA telling her she should have the car keys back. You won't be able to control that.
Your dad is trying to protect himself, your family and others in the community by taking away the keys. He is being a responsible adult.
Make yourself at home and read the sticky posts at the top of the forum. Ask as many questions as needed. Please take care of yourself!