The thing that I've changed is that I've made Sesshoumaru fall in love with Inuyasha's human mother, Izayoi. Or rather, I've made him have been in love with her, only he's very successful at convincing himself that he was never in love with her...getting confusing. Right.
Actually, I've changed more than that, given that I wrote this long before the 3rd movie came out. I'd thought that Inu-papa died closer to when Izayoi died – some time when Inuyasha was several years old. So, to make things more understandable...
Timeline! Consider the "present" to be the time in which Sango, Miroku, & Shippo live, not Kagome's native era. In case you aren't up to date on your Inuyasha episodes, no, this isn't the canon story. This is what happens when someone writes after seeing through episode 106...
67 years ago
Sesshoumaru's father, the Lord of the Western Lands, meets & falls in love with a 20-ish-year-old woman. Inuyasha is born some time shortly therafter. Sesshoumaru, of whatever physical age but the mentality of a 23-ish-year-old, is young, snobby, horny, and (shocker!) passionate. He's of noble blood, and considers other DEMONS to be inferior -- HUMANS aren't worth spitting on. Imagine his shock when he finds himself increasingly attracted to the beautiful human woman his father has (gasp!) chosen for a wife/consort/mate and who has already borne a half-breed child. He calls her "My Lady" very sarcastically, but it turns into a term of (damn!) affection. Inuyasha, already an eyesore, becomes more specifically targeted as the physical barrier between Sesshoumaru and The Lady. What could be more infuriating than realizing that the human bitch affects him? She refuses him. She looks sexy, sexy Sesshoumaru in the eyes & says, "Sorry, I'm already taken." Noooooo! Of course, what he doesn't acknowledge is the fact that he's not only attracted to her; he's in love with her. Her refusal breaks his heart, & he stomps off to parts unknown.
63 years ago
Inu-papa dies. The Lady is killed by Evil Villain XYZ. Sesshoumaru arrives just too late to save her. He melts her body, as he doesn't want her body to be defiled by wild animals, worms, etc. He consciously blames the half-breed brat for her death, as it should be her son's duty to protect her. Of course, Inuyasha is much too young to do any such thing. Unconsiously, Sesshoumaru blames himself, and has to find another responsible party to blame in order to avoid his own guilt. His hatred for Inuyasha becomes absolute loathing. To rub salt into the wound, he receives the Tenseiga a short time (i.e., a couple of months) after melting The Lady's body -- a couple of months too late to save her.
Present
Sesshoumaru saves Rin. Y'all know the rest.