I went to inpatient treatment twice, so my parents were well aware of my drinking. I stayed sober for years inbetween, but then started back and they knew that too. They didn't know that it was getting bad again, though, and so I didn't tell them the gory details. When I got sober this time I just told everyone I decided that even moderate drinking wasn't for me because it was too easy to get dependent on it again.
I say just decide what's best for you. My parents have always been really supportive, but I understand not all families are the same.
Good luck!