Welcome Tinkerweed! First, for your DD, do some searches on this site for book lists/recommendations. There are several threads that have loads of great ideas.
I am very familiar with sensitivities, but I sure haven't figured them out yet! My DS6 showed similar outbursts when he was younger and his drawings didn't turn out how he wanted them, and he eventually stopped wanting to do any art projects or learn to write letters (even though he really wanted to when he was younger). I attributed it to a combination of asynchronous development (he knew how he wanted his pictures to look, but his hands weren't developed enough to do it) and perfectionism, which he seems to have been born with.
The Davidson Institute has some good tips for dealing with perfectionism, written for parents of PG kids but the tips and links work for everyone:
http://www.davidsongifted.org/db/Articles_id_10203.aspxI don't think you're making any mistakes! Parenting is a process. There is a lot of good support and information on this board, and hopefully you'll find something that helps you in some way. Welcome!