She is 3. She is young.
A child's emotions are not even fully developed yet at that age.
The cognition and imaginations, are still developing at that age.
You say you don't want to take the movies away from your child... she laughs while watching them and requests certain movies.
But as you see, at night she has nightmares about it.
So why keep allowing it?
As a kid myself, EVEN at 7 years old, the Disney movies SCARED me.
I did NOT like it. I told my parents. I only watched what I was not afraid of.
Disney movies, are scary. Not all, but many of the "kiddie" movies.
It is for older kids.
Not 3 year olds.
What I would do with my own kids is, I simply told them "that movie is not for your age. Its for older kids." And they understood. I told them some parts are scary.
Now, with a very young child... when there is scary things or violence, they may "laugh" at it, and it is because, they do not know what it means... nor do they understand abstract constructs yet. Nor do they know every nuance of an emotion. They don't "know" how to react to "fear" or "scary" stuff. They don't even know the names of feelings yet either. They don't even know the names of their own feelings yet. Hence, their brain and emotions, cannot process, these things properly. Yet.
But yes, kids from 2 years old have nightmares.
It can be due to what they watch of course.
And it can also be due to: being overtired, not being rested properly, being overly stimulated (physically or emotionally or auditorily, etc.).
And their brains, are still developing. And their cognition, etc.
So, if you don't want her to have nightmares and "so many..." then cut down on what you let her watch. And don't let her watch scary movies.
Disney movies... are scary.
It is for older kids.
The shows and movies that are great and not scary are:
Kipper
Little Bear (by Maurice Sendak)
Upside Down Show
Pocoyo