I had this story in my bookmarks for a while and I just finished reading it a couple weeks ago but I can't remember the name. I'll add what I can remember and hope someone else has luck.
I know that it is complete and rated either M or T. I think Kagome wants to be away from Inuyasha for a while for some reason. Either she's mad at him or wants to get over him because of the whole Kikyou deal. Sesshomaru comes along and takes her to care for Rin because she's sick at his castle. I think the deal was to take care of her in exchange for a place to stay. Once she's healed Sesshomaru has her teach Rin. They eventually get word that Inuyasha is looking for her and Sesshomaru asks her if she wants to go back to him. She says no so they go to...I think the northern lords castle. There is some kind of ball being held for human and demons....where individuals can find a mate. Oh! Before that Sesshomaru had gone and taken Shippo from the group to bring to Kagome because she missed him and was sad, so he is there with her, Rin, and Sesshomaru.
In order to keep Kagome safe it's planned that Sesshomaru will pose as her intended to keep her safe and others from thinking she is available. Inuyasha shows up and fights Sesshomaru to try and take her back. Sesshomaru takes an attack to protect her and she tells Inuyasha that she wants him to leave.
She meets Sesshomaru's cousin while there. I think his name is Shiro or something like that. I believe all of the cardinal lords are Sesshomar's family.
I can't remember when they mate but they do. The war is Sesshomaru, Inuyasha, Miroku, Kouga, and allies fighting against Naraku. Sesshomaru had Kagome stay at the castle with Sango because he wouldn't be able to fight with her around. The cousin is brought to look after the lands and Kagome while he's away. She learns during that time that she is pregnant. There is an assassination attempt on her life because she's human, so they take her to her side of the well until Sesshomaru comes for her.
Kagome's friends and Hojo find out she's pregnant and start judging Sesshomaru because he isn't there and generally making a hard time for Kagome. Naraku is killed and Sesshomaru comes before the baby is born and sets her friends and Hojo straight.
I hope that helps someone find this story.