Dear friend,
As Christians, we are instructed to "speak the truth in love". You viewpoint is absolutely correct. Jesus told us, "Anyone who divorces his wife and marries another woman commits adultery, and the man who marries a divorced woman commits adultery." (Luke 16:18) By analogy, that is exactly what your brother and his girlfriend are doing.
But having said that, I think I detect (maybe) just a little defect in the "in love" part of that instruction. You have said your piece. You were right. But it is not your place to demand that they stop living togther, or really change their lifestyle in any way.
You should not condone what they are doing. But that is no reason to continue to "harp" on the subject. You can treat them with respect and love, and just avoid the subject of their living arrangements. They know how you feel. Your family knows how you feel. It is time to give it to God. Only He can make any lasting changes in their attitudes. Pray for them, that their eyes will be opened to the error of their ways, and that they will repent and leave their adulterous relationship. However, you should not place yourself in a position of openly condemning them for what they are doing. That chore belongs to God.
Finally, if your brother is, indeed, a Christian you might want to call his attention (lovingly) to the Apostle, Paul's warning in 2nd Corinthians, "Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness? What harmony is there between Christ and Belial? Or what does a believer have in common with an unbeliever?" (2 Corinthians 6:14-15) A lot of marriages are dashed on the rocks of unequal belief and faith.
May God guide you in your dilemma.
