I think you should "come clean" with your family because it's possible they will imagine much worse than the truth. I don't think you need to tell them any details about what you did while drunk just that your drinking got out of control and you've decided to stop. I was not close to any of my family and had chosen to live thousands of miles away from them my entire adult life, I had not seen any of them in 10 yrs when I quit drinking and rarely spoke to them, the moral support and encouragement they have given me in the past 3 yrs has been absolutely amazing and a vital part of my recovery even though those thousands of miles still separate us.