I am not familiar with the first story, but I read something similar to what you have describe on Fanfiction.net. I cannot verify if the story is also posted on Dokuga.
www.fanfiction.net/s/5201953/1/No-Such-Thing-as-Fate
Kagome has made the critical decision to leave the group after stumbling over Kikyou and Inuyasha one to many times. Now growing stronger in the feudal era and making it on her own with a fox kit and lessons learned on the way, life just got interesting.
Rated: Fiction M - English - Adventure/Drama - Kagome H. & Sesshomaru - Chapters: 29
I hope this is the story you are looking for. It was written by Silver Phoenix