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 is His slave and Messenger.
Your sister-in-law must be given advice not to take that non-Muslim woman as a friend. The person who gives her advice should be someone whom she is likely to listen to and whose advice she is likely to accept. She should be advised in a gentle and wise manner with good words, and her family should be stern with her and endeavor to bring her back to her senses.
It is not permissible to assume that she is having a lesbian relationship, as in principle, she is innocent of that until proven guilty. For more benefit, please refer to Fatwa 100853. In principle, it is permissible for a woman to kiss another woman, but it is forbidden in cases of suspicion.
Lesbianism is impermissible by the consensus of scholars, and many of them have considered it a grave major sin. The evidence that it is forbidden in the Quran is that Allaah says (what means): {And they who guard their private parts. Except from their wives or those their right hands possess, for indeed, they will not be blamed. But whoever seeks beyond that, then those are the transgressors.} [Quran 23:5-7] If a woman commits lesbianism, then she is definitely sinning.
As regards its prohibition in the Sunnah, Waathilah narrated that the Prophet said: “Lesbianism among women is Zina between them.” [At-Tabaraani in Al-Kabeer and Abu Ya’la - As-Sayooti classified it as Hasan (good)]
On the other hand, the separation of the spouses is not in itself considered divorce as we have clarified in Fatwa 89825. So, if your sister-in-law is still in the bond of marriage with her husband and he did not divorce her, then her going out of his home without his permission is Nushooz (recalcitrance) on her part. The Sharee’ah clarified the ways to discipline a disobedient wife; Allaah says (what means): {Men are in charge of women by [right of] what Allaah has given one over the other and what they spend [for maintenance] from their wealth. So righteous women are devoutly obedient, guarding in [the husband’s] absence what Allaah would have them guard. But those [wives] from whom you fear disobedience — [first] advise them; [then if they persist] forsake them in bed; and [finally] strike them. But if they obey you [once more], seek no means against them. Indeed, Allaah is ever Exalted and Grand.} [Quran 4:34]
If it is not possible to correct her wrongs, then mediators from his family and her family should make a decision for them on their behalf. Allaah says (what means): {And if you fear dissension between the two, send an arbitrator from his people and an arbitrator from her people. If they both desire reconciliation, Allaah will cause it between them. Indeed, Allaah is ever Knowing and Acquainted [with all things].} [Quran 4:35]
The matter should not be left unsettled.
Allaah Knows best.