The husband of your sister who practices homosexuality shall be sinful as well as he shall face the curse of violating the rights of his wife. He should avoid this practice and pass pure and pious life and he should also undergo the treatment of some expert physician till he is able to pay the rights of his wife.
Moreover, it is haram for a woman to develop a relation with any doctor or any other person. She should do taubah from it. And until she is in the nikah of her husband she should think of only inducing her husband. If the husband is not able to pay her rights then it is better that she maintains her marital relation to her husband. The holy Quran praises such women who are pious and righteous and guard their private parts. She should give up the idea of separation because they have two children and by getting separation and by doing a second nikah they might feel difficulties and problems, and next who knows how would be the second husband. But if it is not possible to continue the life and woman fears that she would fall in sin then she can get talaq or khula from her husband. The woman cannot become free without talaq.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband