Ok this one might be a bit of a challenge. I am pretty sure I read it a long time ago on a single spark.

Kagome is a single mother to shippo *I think Inuyasha is the father, but he doesnt want to be involved*. Shippo goes to school where he meets Rin, Sesshoumaru's adopted daughter. I remember one scene where Kagome is driving Shippo to school and Sesshoumaru steals her parking spot right as she is pulling in. I also remember for Shippos birthday she saves up to buy him an expensive book about fairytails i believe. kagome and Sesshoumaru dont get along at first, but because Rin and shippo are friends they see eachother often.

I'll try and remember more if I can, like i said this was a long time ago.

I'm not certain if this is the same one or not but its similar:

Child's Play
Two devilishly determined children with an agenda to hook up their parents and NO ONE will get in their way. Watch out, Sesshomaru and Kagome! Are they truly evil incarnate? No...it's merely child's play! Sesshomaru/Rin and Kagome/Shippo.
Inuyasha - Rated: K+ - English - Romance/Family - Chapters: 5 - Words: 45,030 - Reviews: 88 - Updated: 4-27-09 - Published: 12-31-08 - Sesshomaru & Kagome - Complete

I think this is just really similar, but it looks fun! I'll enjoy reading it! Thanks so much for replying!