It's great that you want to help your mother through this, she will need as much support as she can get. The thing is, you can only help her if she wants help. If your mother doesn't want to give up drinking, theres nothing you can do i'm afraid. She needs to want to quit before you can help.
I don't know too much about adictions i'm afraid, I can only give my own personal opinion but with any addiction, going cold turkey is probably the best option to take. It's extreme, it will be horrible for them and horrible to watch but if someone who has an addiction, such as alcohol abuse, if they have that little bit of alcohol in their system, they will instantly want more. It will never stop at that one drink, and chances are, if they think they are doing well in reducing the amount that they drink, they might decide to drink a wee bit more one day because they can handle it. Truth is, they can't.
If your mum wants to quit, both of you get rid of all the alcohol in the house. You said you aren't around most of the time, thats fine, as long as you support her. Something your mum could do if she decides to quit is, instead of picking up a bottle, pick up the phone and ring you. Doing something like that could help, instead of giving into the craving, talk to someone about it and tell them that your having a problem. It will be difficult to do but that way, she knows that she has her support. I know it might seem like a rubbish idea, but i've used it in the past. I didn't have an addiction problem, it was self harm (thats why i'm anonymous) and instead of hurting myself, I spoke to someone and said "Look, i'm feeling down and want to cut". Having that support really helped me.
For more support, suggest AA. She would really benefit from it.