It's a common mistake: Parent Node
only matters for End Devices. A parent node is the one that buffers the messages for the end-device until it wakes up. So, nothing is wrong with your configuration, routers and coordinators don't have parent nodes, so they always report 0xFFFE (undetermined 16-bit address) for ATMY.
What you can do to determine a topology is to ask/retrieve Neighbor Tables along with Routing tables. It's kind of complex but there is an Application note in this link
that will help you to send and receive these commands.
Let us know if this helped you. Best regards,