How can I create a polycarbonate roof valley?
You will have a difficult time getting approval for a non-traditional material in a roof assembly, code wise.

Additionally, polycarbonate has degradation problems with UV light: City Plastics  

Acrylic or safety glass might be a better choice.

HOWEVER, the real fly-in-the-ointment is the structure necessary UNDER the roof valley, which is not transparent.

Stick with standard roof windows BETWEEN the framing members.  It will be warrantied, accepted by your insurance and code authority, and easily installable by a journeyman roofer.