If the jewish girl who is marrying a goy will never forgive you for not going to this wedding are there any leniencies in this ruling or is it forbidden to attend such a wedding under any circumstance?
Shalom, I am sorry to hear about the tragic situation you find yourself confronted with. Whenever a Jew marries out of the Jewish people, we mourn the loss and pain together with the whole of the Jewish nation. For this reason we do not attend "weddings" of such a nature - for how could one "celebrate" and say "mazal tov" when our hearts are crying and broken? Nonetheless, your question raises a serious issue. The Jewish lady in question will remain Jewish even after marrying out, and because of this we still need to keep connected to her, and hope that she holds on to whatever connection she has with Hashem and the Jewish people. It could be that your non-attendance will push her even further away. On the other hand, your attendance may be viewed as condoning her wrongdoing. Altogether a very difficult question. In general, it is totally unacceptable to attend such a wedding. However if you feel that there are exceptional circumstances in this case, you should approach a rabbi who can evaluate the situation personally. May you be blessed to bring only holiness and good into the world and those that surround you - Blessings.