I am so sorry. For the loss of your dad (I lost my dad suddenly and unexpectedly a while ago - I know the wrenching despair and grief is worse than any words can soothe away), and for your mum. Would she see a GP? It sounds a bit like she is "self-medicating" with alcohol to ease her grief and sorrow. As well as other effects, however, alcohol is also a depressant. She may not be open to it, but perhaps some grief counselling or prescribed anti-depressants might help?
I don't have an easy relationship with my mum and found it hard to talk to her, so sought solace in drink myself. It did not go well. A local bereavement support charity were incredibly helpful, as was my GP and an NHS recovery service called Inclusion, who offered something called SMART Recovery sessions. I am sober now.
As others have said, however, your mum needs to want to make the change herself. It may be that, at 79 and with her lifestyle, this is how she wants to live out the remainder of her days and - I'm so sorry to suggest it - perhaps hasten her journey to be with your late dad. I'm really, really sorry.
Al-Anon, a support service for families and loved-ones of people who struggle with drinking is excellent. You can find them here if you want to: Al-Anon UK | For families & friends of alcoholics. They are kind, supportive and non-judgemental.
I sincerely wish you all the best, and for happier times ahead for you and your mum. x