I believe you are looking for
Something New by sarhea.
Repost from A Single Spark. My own take on what it would take for Sesshoumaru to join forces with the Inu-taichi and for Kagome to leave InuYasha. Take this story as an Alternate Reality set in Canonverse. Where the split occurs is uncertain, just that the Shard hunting group has been pushed to its limits.
Rating: MA - Universe: Canon - Status: Complete - Category: Chapter Stories - Genre: Action, Drama, Erotica, Friendship, Romance - Updated: 01-01-10 - Created: 02-28-09 Chapters: 6 - Reviews: 22 - Words: 20,582 - Reads: 60,357 - Anonymous Reading: Yes