No doubt the emotion is high strung in the matter of a family member's salvation, and I have similar concern for one of my family members to the point of groaning in agony and weeping before God asking for intervention. Paul very clearly understand this desire and agony as he expressed when he said, "For I could wish that I myself were accursed, separated from Christ for the sake of my brethren, my kinsmen according to the flesh" (Romans 9:3). Paul was almost willing to himself be forsaken so that others may be accepted and spared. Moses had the same passion for the salvation of Israel, and if he had not Israel would have been obliterated before they even entered the holy land, saying, "But now, if You will, forgive their sin--and if not, please blot me out from Your book which You have written!" (Exodus 32:32). This a form of interceding deep inside our soul for the well-being of those whom we care for. It often can take the form of wrestling in prayer, and - for men at least - could be the closest thing to child bearing they will ever do: wrestling in their soul in intercession to such a degree and to be agonized with "birth pangs" of the soul, such as Paul said when he wrote to the Galatians, "My children, with whom I am again in labor until Christ is formed in you-" (Galatians 4:19). Paul also passionately beseeched others to come to Christ and not perish with tears: "Therefore watch, and remember, that by the space of three years I ceased not to warn every one night and day with tears" (Acts 20:31).
You have asked a soul wrenching question, and struggle that every Christian must bear for the lost of the world but with God's power in us we can be as Christ to others. But with God all things are possible.
God Bless,
~Josh