Light Cookies with Rotating Sun

Hi, I've got a rotating directional light (sun) that I want to apply a light cookie for fake cloud shadows.
When I rotate that sun to have a day and night cycle, the light cookie (obviously) rotates with it.
So my Question is how do I create cloud shadows with light cookies without them rotating and have natural cloud movement over my terrain?

I already tried to create a second light source, but if I do that, the scene is way too bright.

Thanks in advance!

 

Did you figure out a solution for this problem?