All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Dear Brother, we thank for your ardency and we appreciate your craving after good. May Allah bless you. What you mentioned in your question, no doubt, is a big evil. Since you dislike it, then you are not a partner in that sin. Allah will forgive you, Allah willing. If you are able to change this evil or stop it by preaching that lady to abide by Allah’s Orders, it is better. Allah Says (what means): {Tell the believing men to lower their gaze (from looking at forbidden things and protect their private parts.) That is purer for them… tell the believing women to lower their gaze (from looking at forbidden things) and protect their private parts.} [Quran 24:30-31]
As it is, you should remind your brother and father by a good technique that being with a non-Mahram woman is prohibited in Islam. And remind them of the Prophet’s Hadeeth: “A man should not stay alone with a non-Mahram woman because Satan will undoubtedly be their third (companion).” [Ahmad]
Try to provide your family with good Islamic cassettes and literature. May Allah bless you.
For more benefit on mixing between men and women, please refer to Fataawa 206425, 90256, 217525, 375055, and 133843.
Allah knows best.