Salam Bro,
Those are good links - courtesy of Fi bro. Do check them out.
Other than that, you mustn't break ties with your sister. There are numerous hadith and Quranic verses which forbid a person from doing so. Allah swt, has cursed, in the Quran anyone guilty of this.
Surah Muhammad, Ayat No.22-23
"But if you held command, you were sure to make mischief in the land and cut off the ties of kinship. Those it is whom Allah has cursed, so He has made them deaf and blinded their eyes."
The Worst Deed in the Eyes of Allah
A man approached the Holy Prophet (s.a.w.s.) and enquired, "What is the worst deed in the eyes of Allah?"
The Holy Prophet (s.a.w.s.) replied,
"To attribute partners to Allah."
The man then asked, "After this which is the worst sin?"
The Holy Prophet (s.a.w.s.) said: "To sever relations".
After this the same person asked, "After this which is the worst sin?"
The Holy Prophet (s.a.w.s.) replied:
"To enjoin the evil and to forbid the good (deeds)."
The Holy Prophet (s.a.w.s.) says:
"Do not sever relation with your kindered even if they cut off relations with you." (Al Kafi)
I can understand how difficult all this must be for you. But your sister's actions are her own to answer for. However this does not mean she can blantantly throw her sexuality around in other peoples faces. You can request that she visits you alone and you will be more than happy to see her but that you won't go to meet her where her 'partner' is present.
Remember that not all of the prophet's (pbuh) relatives accepted Islam and therefore remained disbelievers til the end. But the Prophet didn't sever relations with them. What could be worst than denying Allah. Let her know that you love and care for her, but wouldn't feel comfortable going to her place or her coming to yours with her partner. If she is offended by that then just tell her that your doors are always open for her and she is welcome any time. That way you won't be guilty of severing ties with her and incuring sin upon yourself.
best of luck inshaAllah,
wa'alaikum aslam