I'm pretty sure it's a drabble series set in AU/present time. In this story, Sesshoumaru's mother and father are still alive, but divorced and Inupapa has a thing for Kagome's mother.
Kagome hooks up with Sesshoumaru as a one night stand and becomes pregnant. She looks him up in the phonebook to let him know, and accidentally thinks the man she slept with is Inuyasha. She and Kikyo (his wife) meet, in which they find out that the father is Sess.
They try to get to know each other but then Naraku comes back to life to steal the shikon. This is an AU by the way, where Kikyo failed her duty to protect the shikon and her memory was erased, so Kagome and Sesshoumaru's mother have to repeat the battle. While all of this is happening, Kagome has to decide whether or not she wants Sesshoumaru in the baby's life.
I'm pretty sure this story was updated recently and there was something like "Bittersweet" or "Bitter Chocolate" in the title.
The author was saved to my inbox and I just checked to see if they updated the story only to find that my inbox was emptied.