Okay, I have a feeling this is a really famous fanfic, and I'm going to be embarrassed when I find out which one it is: Modern era. Kagome grows up around Sesshomaru's family. When she turns 16 (18?) she goes to England to study under a powerful priestess. She communicates with Sesshomaru over the internet. They are in love, I think, but I can't remember what is keeping them apart. Sesshy being a racist? Kagome being stubborn? I just can't remember. Finally, she flies back to Japan. Then I think they get together after a party to welcome her home. Does this sound familiar to anyone?

I believe its Starcrossed
dokuga.com/fanfiction/story/2206/1?author=4668

That's the one! I never would have found it without you, the title and author did not ring a bell at all! Karma to you!