This is my understanding.
Internet --> Router --> Cat6 --> PC (WORKS)
Internet --> Router --> Cat6 --> Router --> PC (NOT WORKING)
If this is the case, log into the outbuilding router's web page, and disable the function called DHCP. (Usually found under the Lan settings).
You should only have one DHCP server per network.
Please post back to advise if this has worked for you.