Alcoholism Support Group
Alcoholism is the continued consumption of alcoholic beverages, even when it is negatively affecting your health, work, relationships and life. If you think alcohol is causing you to lose control, it's time to seek help. Our group is a safe place to vent, check in, get back up if you fall, and reach sobriety.

I believe there is a genetic predisposition. My dad came from a Scandinavian lineage and alcohol just was not in the culture because it was too cold for the components. They subsided on fish. Now my wife can have one and stop. Her family is German and the genes are different. I see that alcohol has been in the culture for long times. Alcohol is processed differently.
I lied to myself many years and only when I got honest was I able to get free of that hook that had me. The thing that works for me is to just not start, because the obsession is one thing I don't miss, and the shame, and the guilt, and the remorse... Sober is better. I take life and it's trials and cope without having to use booze
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From your case, I'm not sure if you should be worried. Depends on how much gin and tonic you drink. 2 glasses of wine is not excessive. Is it every night? Do emotions dictate your drinking. Do you romanticize alcohol.
You may already know that there's no determining event, DUIs, being drunk in public, losing your job that qualifies you or disqualifies you as alcoholic.
Some kids laugh when their parents get drunk. Others are embarrassed and have bad feelings. It sounds like your daughter really struggled with that event. What's good is you are asking questions and are very aware of a potential to be alcpholic.
Right now from what you described here, it doesn't seem like it.
My father was alcoholic, his father was alcoholic. I am. I'm deathly afraid of my kids going through what I did. They've seen me drunk. My third child has never seen me drink.
Congrats on exploring and asking questions.