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I don't know the answer, but one question comes to mind - What do you have your Max Ray Trace Depth set to in render settings? If you increase that, does it make a difference?
It is most likely normals. In the case of the cube its normals would point outward. With the planes by rotating them both 90 degrees the normals are both pointing forward.
What version of Studio are you running?
Which shaders do which? The default DAZ shader should treat both sides the same, but others may well take account of the facing of the normal - I suspect if you put a plane facing the mirror beyond the "black" plane you may see it, as it may well be that the normal away side is not rendering at all.
The UE dome is, by default, set to be invisible in renders. It's theer simply as a guide, to show you how the environment map is placed around the world, and could be deleted without changing the way UE works.