Praise be to Allah.
Praise be to Allaah Who has shown you the path of guidance; this is a great blessing which you must strive to maintain and give thanks to Allaah for that.
With regard to the issue of your sister, it is important that you strive to call her to Islam and to influence her. Allaah commanded His Prophet (peace and blessings of Allaah be upon him) to start his call to Islam with his own tribe, as He said (interpretation of the meaning):
“And warn your tribe (O Muhammad) of near kindred”
What you need to pay attention to here is the following:
1-Pay attention to making du’aa’ for her, because du’aa’ has an effect by Allaah’s leave. The Prophet (peace and blessings of Allaah be upon him) prayed that some of those whom he was calling to Islam would be guided.
2-Be patient and don’t give up; what is not achieved today may be achieved tomorrow.
3-Use a variety of ways and means (of calling her).
4-Strive to choose appropriate times for da’wah, when your sister is more inclined to listen and respond.
5-Use some indirect methods, such as giving her some moving Islamic books or audio or video tapes, or leave some of them lying around in the house where she can find and use them.
6-Perhaps being related and being together for so long is an obstacle to her responding, so it may be a good idea to look for a religious friend of hers who likes her, and ask her to advise her and try to influence her.
Shaykh Muhammad al-Duwaysh
We ask Allaah to guide your sister, and we advise you to give your sister the answer to Question no. 9465, on the ruling on forming friendships between the sexes, so that she can read it. See also the ruling on homosexuals in Islam, as given in Questions nos. 2104 and 6285.
This calamity which you are living through is a warning to you and to others of the dangers of living in the land of the kuffaar, and it is a motivation for Muslim men and women to return as quickly as possible to the lands of the Muslims.