Assalaamu alaykum. Usually, when I travel out of the country by myself, my wife wants her elder brother to stay with her in the house, and she wants him to sleep in our room while she sleeps in the guest room. However, I am not comfortable with that. Could u give me a fatwa regarding this?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

You have the right to prevent your wife's brother from entering your house in your absence, let alone entering your bedroom. The Prophet, sallallaahu ʻalayhi wa sallam, said, “As for your rights upon them, then they are not to allow anyone on your bedding whom you dislike, nor to permit anyone whom you dislike in your homes.” [Muslim]

An-Nawawi wrote, “The chosen opinion in this matter is that the wife should not let anyone whose presence is disliked by her husband enter or stay in her husband's house (except with his permission) regardless of whether that be a non-mahram (marriageable) man, a woman, or any of her relatives or mahrams.” [Sharh An-Nawawi ʻala Muslim]

Allaah knows best.