I have a player-object and it has a child-object called “HUD” and that’s just a canvas and whenever I rotate the player, with the mouselook-script, the UI-elements in HUD rotate as well and this is really something undesirable and I don’t understand why this is happening.
What could be wrong?
I’ve had this happen in the past. If you’re using a Canvas object, make sure that you change the render mode to World Space. This solves the double-rotation error. I am just taking a wild guess that is what you are talking about 
The other option is to unparent it, and keep it in ScreenSpace - Camera or ScreenSpace - Overlay.
You can write a simple script to unparent it on Start or Awake, if you like it being in the hierarchy for cleanliness.
Hope this helps!