You should be very proud that you reached out. I have an alcoholic mother, it is not easy. But I feel the same as you. Just because a person has one flaw, doesn't mean the rest of them is a throw -away. A mother is a mother.
I have a brother who is very similar to your sister. Does not visit at holidays.
We cannot change these people. We can only learn lessons from them.
And I know that your mother loved you. <3