I have to say that the basic outline and plot is a good idea.  I think I would enjoy this story except for a few things....

Firstly, there is a lot of talking and not much else.  There is not much explaination of scenery, time of day, much about a story is the atmosphere that the characters are subjected to and I don't feel much there.  Usually my enjoyment of a story is increase when I can imagine the characters as I follow it.  Here I can't really see the scene you are trying to set.  So you need more description.

Secondly,  there is not much emotion in your characters actions.  For example when Kagome woke to find Inuyasha a child you could have written something like this:

There was something poking at her, proding and shaking her.  She groaned as she wearily blinked open her eyes.  "What's going on," she asked.  "Miss, miss, I gotta go potty.  Miss, wake up.  Pwease?"

Kagome jolted awake as she noticed just who was shaking her.  A small child dressed in fire rat robes with wide expressive golden eyes, long silver hair, and adorable white puppy ears on his head which were currently pulled back in his distress.  "Inu-Inu-Inuyasha." Kagome stuttered.

The small child head cocked to the side as he looked up at her, "How do you know my name?"

Something like this tells the reader how the characters are feeling in the moment. 

So, that's my advice.  Sorry for taking up so much of your time.

Ciao!

It's... a little dialog heavy. You give such short explinations for what they're doing, and there's real feeling to their words because there is no expression aside from the words. I think it could be much better, if you expanded upon their actions, expressions, and even their thoughts. To put it simply, it's just far to thin... like eating a chicken that was half starved. Still good, I like the premise it's just missing a lot of what draws me into the story.

This story sounds interesting, keep it coming.