I can't really make sense when you use screen, nodes, and image together.
This is the screen I assume you are referring to
or this one
So, let me get this straight. You have an animation but you want to move it to another place within the scene. You cannot just pick up the image and move it because it doesn't contain the animation information it's is probably part of the animation.
The only way you could do this is select everything and create a symbol from selection.
This will take the animation and elements and place them in their own container. You will then be able to move this container (symbol) around wherever you want.