Detachment is not just something you pick up one day and figure out how to do. Recovery is not an event; it's a process. Detachment is a coming to. It's a way of thinking about yourself and the world and your place in it. There are many forms of detachment, physical, emotional, financial.
Just start with one. For me, physical is the simplest and easiest to practice. It could start by deciding you're not going to go to places where there is alcohol with the alcoholic anymore, or you're not going to live with the alcoholic, or when he drinks you will go to another room. It could be not answering the phone when you know he is drinking, or hanging up when you realize he is drunk.
Anger comes when your expectations are not in line with what life is bringing you. Expectations are high when need is high. Look within for getting your needs met. Alcoholics are not known for meeting other people's needs and expectations.