your not getting a reflection from the skydome as you have it at the moment because, as mentioned you have the texture applied to the diffuse, and not the ambient.

I take it, like most skydomes, its quite large. any object that large is not going to be lit by your lighting very well (especially if your using point and/or spot lights!)  also, if your using a standard hi-res sphere primitive to create your skydome, the normals on the object will be facing in the wrong direction. darkning them during render.

generally you want the reflection to be an un-altered reflection of the texture on the skydome. placing the texture on the Ambient node ensures this happens.

TemplarGFX
3D Hobbyist since 1996
I use poser native units

167 Car Materials for Poser