I have a VHD that I suspect is a differencing disk. How can I know for certain, and if it is, then what parent VHD is it tied to?
This is most easily done by writing a script that looks at the VHD through the WMI provider for virtual storage.
Look at the Msvm_VirtualHardDiskInfo values.
For examples scripts that deal with Hyper-V, and particularly the storage classes, see Ben Armstrong's blog: