(scratches head thinking...)
Maybe try this:

Go back into the atmo editor, click the Light Tab:
Reduce Light Intensity to around -45
Raise Light Balance to around 75%
Change Ambient Light Color (dble-click the color) and make it a DARK MUTED color (browns or maybe blues).

Now click on the Clouds Tab:
Reduce Global Exposure and Global Illumination - don't have to go far to see the diference.

Back out to scene:
Add a couple of Spotlights shooting in close to the same direction as the sun AND:
1 - Disable their Lens Flare (little "star" icon at upper left of the properties box where you normally see/pick your textures).
2 - Widen the cone angle to maybe 50 degrees.
3 - widen the Fallof to maybe 60% - don't worry, it looks great - or at least it's a starting point for play.
4 - Make them at 50% softness so their shadows don't compete with the sun's.
5 - change their color to either match or augment the sun's color (warm or cool tone in like with the sun).
6 - Raise their Power level - try 300 as a start.

Now do a test render of a single frame and see what you think. - you don't have to do multiple frames - just one to see how it's gonna look.
Adjust where you want - it the shadows are too dark you can up the Global Illumination or Exposure, or add soft lights to fill them in like a cinematographer would. You can even add hard brighter lights to have "shimmers" and backlighting for more dynamic looks.

Hope this helps - good luck!
-Lew ;-)