You don’t need any of that stuff 
If you want to rotate the sky, you can just add to the UVs in the sky material. Assuming your texture is square
The reason you’re getting distortion, is because the typical sphere has distorted UVs, especially pinched at the top
The other option, is a sort of cube layout, but then the distortion is just somewhere else
In the end, the best option, is to make your own sky dome ( not sphere ), because it is possible to project the UVs down from a plane, and avoid almost all problems
Here I just made a sphere using the modelling tools, and then reprojected the UVs using a plane. Tell me if you need a step by step on that.
As long as you keep the stretchy bit low on the horizon, you’re good.