I agree that you are being a bit over protective. I'm guilty of it too. But having some scary moments , like Sleeping Beauty, will help her learn how to deal with fear. Right now you may not be teaching her how to deal with scary issues because you're avoiding them. I've allowed my 7 year old son to see scary things but with me next to him to remind him this is pretent, you have nothing to fear from a movie, or teaching whatever the situation in the movie is I'll remind him thats why you shouldn't do whatever the movie is doing. Like in Snow White the witch scared him, I talked to him about accepting things from strangers and how it can be bad. He is a very confident kid and is not scared by much.
I think allowing your daughter to experience fear and guiding her through it is best. Good luck !