I don't think we're ever called to give up on family. We are called to love Christ more than our family and in that respect He means that we aren't to choose them over Him. For example, if you're family wants to go out and have a wild night of partying, you are to deny your flesh and not go along. However, this doesn't mean that you aren't there if they call too intoxicated to drive and want a ride.
It is all about discernment. Basically, don't do things that are unholy and un-Christ-like just because your family does. Our family needs the example of our love and right living in order for them to see the truth and they also need our prayers. Remember that the Bible says that if a spouse is unsaved but wants to stay, the saved spouse is not to put that spouse out.
Back to discernment, if there is danger to you, if their is danger to the other person or other family members, by all means, do not be around them, however, you must remember to pray for them and seek God for their salvation, that their eyes be opened.
Jesus tells us to forgive 70x7 in a day. He wants us to shine with His love. The deciding factors are 1. are you allowing them to distract you or pull you away from intimacy with Jesus and 2. are they a danger to themselves, you or others? If neither of these are yes, then I would say you are not to disown your family.
Sometimes, addicts can destroy relationships due to their addictive cycles and their constant using of their family members to bail them out. Since this harmful to themselves and to others, this would fall under the first category.
I hope I helped a little. God bless.