Sorry for the long post but as a recovering alcoholic I pretty much agree with everything you said. I was addicted to alcohol but have been sober for 3.5 years and hope I can provide some insight as to why I agree with your statement that an alcoholic who is now sober is making a choice when they start drinking again.
When I started drinking at the age of 18 it almost immediately became an addiction. I made the choice to drink at first, of course I did, but after a few months it became a compulsion that was incredibly difficult to stop. I was desperate to stop drinking but couldn't force myself to stop, the addiction had such a strong grip on me it literally warped the way I thought. I was drinking in the daytime, in the evenings by myself, secretly away from my family, every single day. It was ridiculous and I knew it was but the addiction had an incomparable control over me that I can't even describe. Looking back in hindsight I can't believe how much I was out of my own control, everything I did and the entire plan of my day was focused around alcohol. It's embarrassing to admit this but it's better to be honest.
Before I joined AA, there was a period where I realised I clearly had a serious alcohol problem that was spiraling and getting worse much faster than I could keep up with it. I was at risk of losing everything but stupidly felt too ashamed to admit anything to my family or friends, so I'd tried to become sober myself and I managed 3 months of sobriety before relapsing. I realise now that I hadn't really "remedied" the addiction and had just suppressed it, so after time the thoughts came crawling back of "I'm cured now, I can just have one or two drinks", before "well one bottle of wine won't hurt, I've been sober for ages!" etc. It was absolutely my choice to drink again but the addiction in my brain had been drip feeding me ideas for weeks, it's bizarre to look back on and admit to but I'd literally convinced myself it wasn't an issue anymore? I thought I'd fixed it so I could now start drinking like a "normal person", which I can now see was fucking ridiculous but at the time I thought this was totally reasonable.
I then hit rock bottom, joined AA and I have now been sober for over 3 years. I told my partner, parents and friends everything so I became accountable for my actions to someone other than myself. I admitted my inability to control my alcohol consumption and knowing what I do now, I will never drink alcohol again.
I know that if I make the choice to drink again, even a small amount, I will lose the ability to control or stop my drinking. When an alcoholic has been sober from drinking but then start drinking again, it's a choice to pick up that first drink. Alcoholics know the impact alcohol has on them, they know they can't control or limit their drinking, they see the impact it has on themselves and their families. While stopping drinking as an alcoholic in active addiction can be incredibly difficult and, for some, impossible, once an alcoholic has been sober and has seen the positive impact on their life, their health and their loved ones, the decision to start drinking again is a choice they make. They often make this choice knowing that they will soon lose control again.
Why they make the choice depends on each person I suppose. For me, it was the fact I'd managed to listen to the addictive part of my mind and literally convince myself I was never a proper alcoholic to begin with and I was cured and it would all be fine. This was obviously a load of shit and I nearly died as a result of my drinking from this relapse. Even now, 3.5 years deep into sobriety I still sometimes get those addictive thoughts pop up in my head. The "no-one would know if I just had one", "it would be so nice to have a glass of Pimms on this sunny day", "you've been sober for 3 years, one glass won't hurt!" etc, but AA helped me recognise these thoughts and identify them as exactly what they are - my addiction. It will always be there in the background for the rest of my life, no matter how long I've been sober.
Having the coping strategies I do in order to deal with these thoughts properly, it would be MY CHOICE if I chose to listen to them and pick up the bottle, but instead I choose to deal with them correctly. Your mother did make the choice to start drinking and I am so sorry she did this, you are completely right to go NC, an alcoholic can never be helped unless they genuinely keep wanting to help themselves and devastatingly, sometimes they simply don't want to help themselves. Some people never admit they are an alcoholic and go along with the help and therapy to please their loved ones. Other people know they are an alcoholic but don't want to stop drinking. Either way, you've made the right decision but I'm so sorry it was a decision you had to make in the first place.