You know, I think I was looking for the same story recently.
Same background. He looks after Rin's descendants and seems in some way to be "honor-bound" to protect the family (answering to any family member, but the head of the family in particular). He's kind of like an inheritance.
When he finds Kagome he's currently serving a woman who heads the family, who has a son who is a brat and a pain in the ass who Sesshomaru often has to get out of trouble. They know he's a demon of course.
Kagome does end up staying the night, and they do sleep together, but it takes a long time for their relationship to reach that point. It was a great story, and unfinished the last time I read it.
Ok, now I want to know where the heck it is too.
). Of course, he told her "no" right off, but she was able to talk him into it eventually. (Geez, I read too much fan fiction 
).
