You can look at your family in one of two ways: either as a problem you can't solve–or as an opportunity to help some find the right path in life.
Which way does God want you to look at them? I think you know the answer. After all, if you turned your back on them, would anything ever change? Probably not. But God has placed you in this family for a reason: so you can point them to a different way of living through a personal relationship with Christ. Jesus said, "You are the salt of the earth. ... You are the light of the world" (Matthew 5:13-14).
Remember: God loves them just as much as He loves you–in spite of their sin and their chaotic lives. He loves them so much that He was willing to send His only Son into the world to die for them. And if you are a Christian, He calls on you to love them the same way He does–even if they aren't very lovable. Jesus said, "By this all men will know that you are my disciples, if you love one another" (John 13:35).
Pray for your family, that they will open their hearts to Christ and discover the joy and stability He alone can give them. Then ask Him to help you be a witness for Christ, both by your life and your words. It may not be easy and your whole family may not change–but if only one finds Christ it will be worth it.