You might not be able to use SERVERNAME\INSTANCE when creating the linked server. try SERVERNAME,PORT. This may be because the SQL browser service is unable to cross your domains. I had this exact situation previously and just used the servername,port notation with the linked server.

By default the ports for named instances are dynamic and can change after every restart so if you haven't configured static ports for your named instance you would either need to get SQL Browser working across the domains or configure a static port and use the servername,port notation.