It isn't so much he cares for her. He has apppearances to maintain.
Rin comes to Kagome asking her to teach her the "womanly arts." (Self-challenge fic to see if I could write yuri.)*winner of the Feudal Association's best Yuri fic*
Rin runs into a pretty interesting scene. What happens when she asks Sesshoumaru about it? Oneshot. Daughterfather scene.