The best thing I believe you can do is love your family as Christ loved the church. I can give you a personal example of something similar I have dealt on with my family.
I came from an unsaved background. No one in my family had known Christ when I was saved, except for my wife. This was a little over 5 years ago. Once I was saved, starting that very day, I became a zealt for the Lord. Anyone and everyone I talked to, I talked only about the Lord.
I was saved at around 4:00pm. My wife and I went to have dinner at her parents house at 5:00pm. The zeal for His house had consumed me. All I would do is talk about the Lord. Everything. Anything. All was about Him. This continued for about 2 years.
After a while my wife began to tell me that her parents and siblings didn't like me very much. They would be passive aggresive to me and shun us as "the weird siblings" and such. Much hurt was felt by my wife and I. Even our children were shunned as such by the family. It was pretty dark when dealing with her family at this stage.
Around this time, the Lord lead me to just be quite about Him and only love on her family. Love, love, love. The only way I would talk about the Lord, is if they would bring Him up, which was VERY rare. It pained me so much to sit there with my wife's family, and not be able to share with them the love that I knew because of Jesus, but I had to obey what the Lord placed on my heart. So I loved them for who they were, not for who I know they needed to be. It was very hard, but fruitful.
A funny thing started to happen about 2 years ago. My wife's family started to open up to the Lord. My wife's sister started to ask us about our House Church. She stated to see that were they were going to church was bearing no fruit. It was in essence, a place without the Lord.
My wife's sister then asked if her family could attend a House Church that we are affiliated with. The man who lead this House Church that she wanted to attend, is the same man and wife who discipled my wife and I. My wife's sister and her husband began their journey.
Lots of things started to happen. My wife's sister came to the Lord, her mother and father started going to church. Even her younger brothers started to go to some church meetings for young adults. The Lord began to draw them in on His terms, not my own.
Something cool has happened recently on this subject. My brother-in-law and I just went to serve a short term mission trip at an orphanage in Mexico in January this year. While we were there, my brother-in-law stood up in front of all the people we went on the mission trip with and thanked me for being a great aexample to him and his wife. He stated that if my wife and I wouldn't have been such a good example of Christ, that he would have never come to the Lord. He said that he thought that my wife and I were crazy for many years, but know he sees that we were not. He thanked me for being a light to him and his wife, and said he was sorry for how he treated and thought about us...
My friend. Do you see what I am saying? Love on your family. Love them without question. It will be hard. You and your family will be insulted, mocked, looked down upon, though of as crazy, shunned, etc. But it is all worth it. Don't get into theological debates with them. Don't stop hanging out with them (unless it is blatent sin), don't stop calling or trying. You may be the only light that is in their lives. But do all of this with love.
Love your family. Love them like Christ loved the church. Your love will be the best witness of Christ that you may ever give them. Love them, and let Christ do the drawing. Only the Lord can call them into His kingdom. Your job is to love.
I do not pray for these alone, but also for those who will believe in Me through their word; that they all may be one, as You, Father, are in Me, and I in You; that they also may be one in Us, that the world may believe that You sent Me. And the glory which You gave Me I have given them, that they may be one just as We are one: I in them, and You in Me; that they may be made perfect in one, and that the world may know that You have sent Me, and have loved them as You have loved Me. Father, I desire that they also whom You gave Me may be with Me where I am, that they may behold My glory which You have given Me; for You loved Me before the foundation of the world. O righteous Father! The world has not known You, but I have known You; and these have known that You sent Me. And I have declared to them Your name, and will declare it, that the love with which You loved Me may be in them, and I in them.