Thank you. We don't give her false hope because we know that it is pointless. Hope is something we all cling on to when faced with adversity, but alcoholism (or indeed any addiction) cannot be given hope until such time as the addict admits they have a problem and actively starts helping themselves. Mum is nowhere near that stage, as her friends have been telling her for a long while she is sick, but she denies she even drinks, let alone doing something about it.
We think it would be good however for my stepdaughter to write her mum a letter. Not to beg her to stop drinking because she knows that won't work (not to mention, as you say, the guilt she would shoulder because her mum won't take any notice), but to tell her mum she knows what her problem is, knows she is an alcoholic and to tell her how SHE feels about it, how it has affected her life thus far. She is quite low today following mum's visit yesterday, and it has shocked her to see her mum so yellow. Of course she is worried about her mum, that's to be expected.
The road we are travelling is a long one, and I agree, counselling needs to be put in place as it's gonna get a whole lot harder!