Hi,
On both port connecting Core_A to Core_B, you have to transport Vlan20.
1st: Switch your interface to trunk (port link-type mode trunk under interface configuration).
2nd: Allow both Vlan10 & Vlan20 (port trunk permit vlan 10 20).
Then, on Core_B, you can configure interface connected to PC on Vlan20.
If you still have issues, please, provide the full configuration of each Core (dis cur).
Hope this helps you
Jean-Christophe