In computer graphics, if you want to get "daylight" illumination for cheap, you simply use two lights - one white-to-yellowish directional and one bluish hemispherical:

http://threejs.org/examples/webgl_lights_hemisphere.html

You only compute expensive scattering if you need volumetric effects (e.g. god rays or atmospheric fog blueing things far away, on the order of at least hundreds of meters).

But here for simple indoor lighting, you don't really need volumetric effects. You just need proper light color coming from roughly appropriate directions - one strong white-to-yellowish light (coming from uniform direction) that will cast hard shadows and one weaker bluish diffuse light (coming from many directions) that will cast soft shadows.