Bethesda did not play-test or consider many features they included in the game. While it is better to include them and let the players fix them, it is also at times baffling how certain things are allowed to be as they are.
Skyrim does not have animation smoothing nor does it have animation morphing. As soon as you move the mouse enough for it to send a move-command to skyrim; the game will start playing the turn animations.
If the difference between the idle animation and turn animation are different, then a "jerk" will be played. Not a big issue on a controller. Impossible to miss on a mouse.
Find every idle animation file that is associated with a turn animation. Then copy that idle and rename it to xxxxx_turnleft60.hkx and xxxx_turnright60.hkx
This will work for any animation mod. Just make sure that the file-structure is Data/meshes/actors/character/animations
I do not use vanilla animations. They are simply included as an example to other people who are looking for a fix.
Remember that the sneak-weapon-drawn turn animation is a combination of the idle of whatever weapon you have equipped. So find animations that work in multiple positions if needed.
Aside from the already mentioned sneak-turn issue. The player character will ice-skate unless you turn quickly. Without a new animation engine, there is no work around for this. Putting the turn animation as idle will see the character ice-skate without pause, since the animation will play like a youtube video regardless. And blah blah jadidaah.
It is just renamed vanilla idle animations. So, no scripts, no nothing. Place below mods that add animations. Or better yet, compile your own archive of animations and use this "fix" as described under The Sollution.