No, you shouldn't forget it -- both for their sake and for yours. Admittedly, it may not be possible to restore your relationship with your family -- but that shouldn't keep you from trying. The Bible says there is "joy for those who promote peace" (Proverbs 12:20).
What can you do? First, let them know that you regret what happened, and that you know you were in the wrong. Don't dredge up the details of the past, however, or try to play the "blame game"; what they need to hear is that you're sorry for what you did, and you hope they will forgive you. Incidentally, a letter will probably be more effective than a phone call. If some of them respond positively, you can follow up from there.
At the same time, they may be suspicious of your motives, or even be afraid to become too involved with you. Remember: It takes only a second or two to break a bone, but it takes months for it to heal. The same is true with relationships -- and in all honesty, they may never be completely restored.
The most important thing you need to do, however, is to seek God's forgiveness for the past. Our sins may cut us off from others -- but most of all they cut us off from God. But God loves you, and Christ died to make your forgiveness possible. Open your heart and life to Jesus Christ today.