You have created an argument with your light sources.
First, you must not have my book because if you did, you would never adjust SUN color with the "K" degrees setting.
1: Realistic sun should have 0.0 divergence for sharp shadows.
2: skydome energy will always soften a shadow.
3: Fastest rendering is with the SUN SUN in the Photorendering Dialog with high - like 200% - ambient and no skylight.
4: If you have results than cannot be adjusted, there is probably a stray sun object or something on another story that affects the scene.