I can only remember a little. It was set in the fuedal era and Kagome is either visiting or living at Sesshoumaru's palace. Sesshoumaru has a cousin and I think her mate treats her bad so she is always sneaking out to visit Sess. She really likes Kagome and is trying to get Sesshoumaru to mate Kagome but he is reluctant for some reason.

Isn't that the one where the cousin doesn't get along with InuMama and snubs her, InuMama even attacked her at one point (I think, as long as I am not confusing it with another story)
I think the cousin's mate was an obnoxious being that at one point tried insisting that she return back to his land to him, but she was staying in the West at Sesshoumaru's palace to avoid the creep.
Wish I could remember more about this story, but maybe that will help jog someone else's memory.

I'm not sure about the Sessmom part, but I think you are right about the cousin's mate. I think it was a political mating and they had some kind of agreement that he would be faithful to her but he's not.
I remember that her personality was the total opposite of Sesshoumaru's