OP<
I think the question behind your question is whether you should forgive your father. If alcoholism is a disease you think you should but don't want to; if it's not a disease it's okay to stay angry with him.
I think that you would be better to separate the questions. Even if it is a disease, you are understandably hurt, angry and sad at how much damage she has caused to the lives of people you love, including yourself. That is completely understandable and normal. And it takes a very long time to get over it. It is better for you and your family, however, that you do get over it. Hard to do, I know,if she's still in a position to cause damage. You need to minimise the impact on yourself and your own family and get some distance. Perhaps join a local meeting for families to get a different perspective and some support.
On the other question, yes alcoholism is a disease\illness,and one that damages the alcoholic's ability to reason, to choose in a rational manner. To say that it is an addiction does not mean that it is not a disease or illness. Some diseases are mild and leave no lasting effects, others are fatal or potentially so. Your parent didn't choose to have the genes that gave her an addictive personality or )possibly the environmental factors that switched on the genes. As to choosing now, her ability to reason and to recognise what she is doing is virtually nil. Alcohol is just the main drug that our society prescribes to addictive people. In different circumstances, it could have been a different drug.
If she had had slightly different genes she might have been depressive or sufferred from other identifiable mental illness. When we know more about the brain we'll perhaps know more about the causes, which might be the first step to a cure, but for now there is nothing that your or your family can do except accept the situation. It is very sad.