In an architecture where you have multiple policy server connected to individual policy store and individual key store, if you want to do Single Sign On between the different policy server / environments. You need to make sure that all Policy Server will share have the same keys.
In order to have SSO between your 2 environment (multiple Policy Store with separate key store) you should set the same static key and session ticket key for each policy server.
You can check the following documentation:
Policy Server Guides : Policy Server Administration Guide:
Configuring and Managing Encryption Keys : Key Management Scenarios: Multiple Policy Stores with Separate Key Stores