My Cat Just Threw Up A Very Very Long Thin Moving White Thing. It Maybe A Worm I Don't Know It Is Disgusting. I Take Her To The Vet Like She Is Suppose To All The Time And The Shots Are Up To Date. What Am I Doing Wrong?

First of all, you're doing nothing wrong :)    

From your description, it sounds like "roundworm" which can be easily treated with a multi-wormer tablet like Drontal from your vets.  It can two or three doses over time to completely rid the problem.    

Here's an article on the different worm types cats can have :
www.petmedsonline.org  

this article is specifically about roundworm (very common by the way)  
www.dr-dan.com   

Enjoy your cat! You sound like you're doing everything right :)