Disclaimer* I didn't read the responses so far, so this may have been said - since this forum is full of smart people! (see what I did there?)
I'll bet there is someone else in your family who takes secret drinks too.
This is about you. You don't have to tell your family you have a "problem." Just tell them you've had enough of drinking, you don't like it anymore. It's the truth.
Then just repeat as often as necessary, "No, thanks, I don't drink."
You have no obligation to tell anyone why you've stopped. It's not a lie to say you don't like it, or you've had your fill. You don't have to label yourself an alcoholic. I tell people I don't like it - they can draw their own conclusions. I don't really care what conclusions they draw; it's none of my business.