Heehee, this is a most amusing parody. And whenever I saw "Uaaaan" in this chapter, I felt the need to say it aloud, because it was funny.
You know how to make a parody actually funny, which is awesome. Most parodies end up making themselves indistinguishable from actual badfic.
I only noticed one thing, which is very minor, but would bug me if I saw it later in one of my stories and nobody pointed it out to me. In the third chapter, you use BIT where I believe you meant BITE ("She understood that yes, he was a dog demon, and therefore had some dog-like "urges", but that didn't give him an excuse to BIT her!"). Probably just a typo.
Sesshoumaru's a very quintessentially sexy, mysterious, violent, possessive, yet ultimately caring and gentle man. XD