I understand why they were out of character. We don't really know much about Midoriko except for she was a powerful priestess. And Sesshomaru is centuries younger then he is in the Inuyasha storyline.
I enjoyed this story. It's totally believable that Midoriko would have met Sesshomaru a long time ago, after all we don't really know how old he is and we don't really know how long ago Midoirko was alive. I think it'd be cool if you updated, but this chapter could stand as it's own oneshot if you wanted to leave it that way.
Anyway, great job!

This reader found the story most enjoyable.

Wait...da fuq did I just say?

Damn it, I'm in such an Inuyasha mood that I'm starting to imitate my fave character, namely Sesshomaru.

A good start. Not many people are interested in tackeling this pairing, so I look foward to the rest of the story.