Instead of taking her drinking as the problem, take her reasons for drinking as the problem. Alcohol... 90% of the time... is for escapeism. Either to escape the downsides of "real life", or to create a false image of yourself. For your mum, its the first thing. There's nothing you can do to stop it, but you can start by realising the drink is making her ignore you and your sister - it's nothing you've done wrong, and it's not even your mums personality to do that. It's completely down to the drink, so don't feel that there is any blame to be placed.
Secondly; your mum must be very unhappy at the moment. I assume for the reasons you told us. Maybe you could just ask her how she is, randomly during the day (when she's sober?) - she'll realise you're concerned for HER, and not her drinking.
Good luck and stay strong
