Sadly, it's all too common for alcoholics and 'drink-dependent' people to be in strong and continual denial to themselves as well as everyone else about just how much they drink. However, your SIL's mum's GP is probably pretty clued up that his patient is a heavy drinker, just from her general state of poor health, but may not realise just how much perhaps? He may have mentioned the advisability of 'cutting down a bit' but these days it's not 'the custom' for GP's to be as blunt as medically at least they need to be about our rubbish lifestyles! Even obviously obese people just get 'advised' to 'cut down a bit' etc etc etc.
It probably doesn't make any difference, however, whether your MIL's GP has been blunt about the medical need to stop drinking, (assuming he realises just how much she is!), since whether he's blunt or not is unlikely to have any effect on your SIL's mum's actual drinking! (which perhaps is why GPs don't bother to make an issue of it, as they know bitterly we still won't change our unhealthy lifestyles!)
May be the only realistic thing now is for your SIL to accept that her mother's drinking will be shortening her life and adding to her medical deterioriation. That said, if giving up only adds 'a bit longer' to her life expectancy, and doesn't much improve her current quality of life, is there any point in going through the grim process of coming off alcohol?
People don't become addicts without their usually being strong psychological factors involved in driving them to addiction, and unless these are sorted out, quitting is unlikely to be successful anyway?? Plus, of course, there is all the question of denial, and the anger that comes when others try and get the addict to accept and recognise that they are alcoholics - especially when they have a lot of alcohol in them. (My SIL, who became 'drink-dependent' when caring for four years for her mother with dementia, gets extremely angry and aggressive if you try and stop her drinking after she's already consumed a bottle of wine in a night! And she gets pretty angry if you tackle her about it when she's sober.....in fact, to my mind, 'anger' is her predominant emotion, and what 'drove' her to drink in the first place, anger at the life she's had to lead, and anger in particular about being 'landed' with her mother's care needs, even though her mother has now been dead for a few years. The anger and the drink dependence are 'embedded'.)
I guess what I'm saying is that although I'd say that your SIL should probably write to her mum's GP making clear just how much his patient is reliant on alcohol and how much she is consuming, in practical terms her addiction may have to be something that is simply 'managed' rather than eradicated, given her age and other health problems.
Sadly, supporting your SIL is probably the best you can do now - she's in for a grim time I suspect, and having a good friend and family support in you, if that is your relationship, I'm sure will be a comfort and practical help to her.
