If your husband quits drinking but you don't trust him and his family doesn't understand why won't you take him back?

You are not obliged to take someone back for any reason, it always remains your personal choice who you are in a relationship with. If the marriage is worth saving, counselling is something that helps many couples. His family may assume that the only reason for the split was Alcoholism but even if he is no longer alcoholic there is no law that says you can't continue to be separate, after all you could have moved on in the meantime. Be polite, but if they hassle you about this you are within your rights to tell them to mind their own business.