The distinction is very vital. George Washington, for example, pointed out that our system was rooted and depended upon private morals. That did not mean that he advocated a host of new laws intended to make people more moral--exactly the opposite. He understood that people who did not have the moral fibre to regulate their own conduct in accordance with a system of moral values, could hardly be trusted with the affairs of State--or with handling your business or commercial interests, either.
There is no need for you to explain a conflict between your traditional Conservatism and Libertarian values. There is none. Your family might have erred in the direction of going overboard in tyring to protect social morals, or they might not have. But that involves other issues. My point is that there is no reason for any divide between the Conservative and Libertarian bases of America, over morality.
William Flax Return Of The Gods Web Site