You have already lost your mom...I think that is what you are realizing. You lost her to alcohol and nothing you say or do will change that. It's like a death and you are grieving. I went through that with my own mother, who was a raging alcoholic for many years. Unlike some here, I could not look past all the hurtful things she had done, especially to my daughter and g'children. I totally cut off communication with her years before she died. I only found out a year after her death, through an online search, that she had died the year before at the age of 82. I could not believe that she lived that long with the drinking she did. I suspect that she must have stopped at some point. However, in medical records I obtained, I learned that she was very senile. She actually died of a heart attack. It would have been easy enough to find me, had she wanted to. However, I've never regretted my decision--only that her alcoholic thinking and behavior made it necessary. Sometimes we have to let go...it's the only way we can live our own lives.
Looking at the situation realistically, and accepting how it is, is the first step in letting go emotionally. Then you are no longer hurt by broken promises, etc. How involved you want to be after that, is up to you.