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.
We do not know why this woman does not want to stay with her mother who is still alive. Neither do we know why she is interested in living with her brother in a western country, even though it may cause problems between her and her sister in-law.
However, staying overnight alone is not desirable for men. Ibn Abu Shaybah reported in his Musannaf from ‘Ataa’ that the Prophet forbade traveling alone or staying overnight alone. (This is a Mursal Hadeeth).
Abu Ja’far, another narrator, reported the narration with the following wording: “Do not spend a night alone in a house because Satan will be very fond of you.”
‘Umar said: “No one should travel alone, and no one should spend the night alone.” [Al-Albaani: Sound]
Therefore, if staying alone is not desirable for men then it becomes more emphatic for women. However, staying alone overnight is not forbidden if it does not lead to any temptation or bad consequences.
Moreover, if her stay with her brother causes any harm to him or to his wife, then she is not permitted to live there. The Prophet said: “There should be no harm, nor reciprocal harming.” [Ibn Maajah]
If there is no harm, then she can live with them.
Allah knows best.