um... Yagyu is the his surname Jubei is his first name. The daughter's name would be Yagyu Jiyuu no Jiyuu Jubei. Also, Jubei-sama really does have a daughter. Two in fact. One who is a character in the second part of the Jubei-chan series. Her name's Frecia or however the heck it's spelt.

Just so you know: Jubei is not the last name of Yagyu Jubei. Yagyu is the family name, Jubei is *his* name. Japanese names list them in that order. :) So the person mentioned in your summary should be Yagyu Jiyu.

First off, it is fantastic to see authors attempting Jubei fanfiction. I think it is a little read genre in that it is a little known anime.
One suggestion for your fanfic would be to try to mimic the feeling of Jubei a bit more - full of akward moments, general chaos and confusion, time of determination, and mostly just plain silliness.
You've got a good start!