Okay, that is not a problem.
Uhhh... in case you don't know it, there is not something called "day-night cycle" in the SFS Planet Editor, so we have to improvise. Most of us make DN cycles with just clouds. So what you see in the background during the night is not a special night texture, is just space, like if there were no atmosphere.
That being said, I must reply that darken only the night is simply impossible. You can dark things up with Post Processing, but that will apply to the whole planet, not just to a section (the night), and will definitively won't rotate around the planet.
So... honestly what you request is impossible.