Most Witnesses are ignorant of the current views from the Governing Body, as things change often. As a result so see things as if they had taken a snapshot of their beliefs when they were baptized, and keep it as the basis of how they view the Bible throughout their lives. And there are others who have never bothered reading their Watchtower study articles thoroughly and only pick up the highlights, misunderstanding things along the way. So we should expect to encounter those like your family, who aren't in tune with current doctrine.
But to answer your question about Jesus and sin, more directly. Biblically you are 100% right, however because the Organization has chosen to push Jesus into the background (in favor of underlining the name of God), Jesus' roll is not generally elaborated at the meetings or discussion articles. The example of King David get more air time than Jesus actually. Thus even from this angle, we can see why Witnesses may be ill informed about the Messiah's place in our lives.