Yes, in the original story, her name is Florine. However, the version of the fairytale I've heard is different and comes from a book of French Fairy Tales. Princess Florine's step-mother is an evil Queen (like in Snow White) who has an ugly daughter named Troutina. The Evil Queen invites princes and suitors to meet Troutina, but they are always captivated by Florine. A particular prince meets Florine and pledges his love to her. This infuriates the Evil Queen, so she sends a fake message Florine to the Prince asking him to meet her at her window. He meets her and tells Florine that he would like to marry her and puts an engagement ring on her finger. But in the darkness he could not tell that it was actually Troutina in disguise. The Evil Queen tells the Prince that he must marry Troutina since the ring is a symbol of a binding agreement. He refuses, so the queen has a sorcerer turn the Prince into a bluebird and hold Florine captive in a tower so that she will no longer have a problem with her stealing potential suitors from Troutina. However, Florine is still in love with the Prince and he comes to visit her every night. She sits at her window listening for his song.
I know what you mean about the tremor like movements with the hands. I could only get my right hand to do them, so I just had to leave them out. (It's actually very difficult. I think it might be like rolling your tongue, something that some people are just genetically predisposed to.) I'm actually going to be restaging a version similar to the Royal version soon. It's the Sadler Welles pre-Royal version, actually. The only thing I'm changing is I'm taking out the ending leap off stage at the end of the Coda.
Cris