Thanks for your question.
It is good for you to be concerned about the members of your family. However, the relationship of your father and brothers to God and the hope of the Gospel is up to them. They have to make their own decision and will stand or fall before God on that basis. [Psalm 49v.6]
What can you do? Two things - pray for them, and set a good example of faith and behaviour. People do not like being preached at but they will be impressed by a consistent and loving example of faithfulness and caring.
What will happen to my unbelieving family when Christ returns? That is best left up to God. If they do not believe but are alive when the Lord returns, they may well have the opportunity to live as mortals in the Kingdom of God during the millenium and after that, if they have been faithful themselves during that time, to inherit eternal life.
The main thing for you is to have faith that, whatever happens, God will always do the right thing. [Genesis 18v25]. Let that knowledge lift the burden of anxious care you have been feeling. Be happy that such issues of judgement are in His loving hands. Your job is to witness not to worry.
God has not given up your family. It may just take more time than it did for them to believe the Gospel than it did for you. In the meantime, pray and set a good example and do not worry about the outcome. Your joyful faith will be a powerful witness but anxiety will be counterproductive.
I hope you have found this helpful.