bitcoind is refusing to connect to my other server
By default bitcoind only binds RPC to the loopback interface, so you can only connect to it from localhost. This is for security.
You can allow connections from a specific other machine with
-rpcallowip, or in general with
-rpcbind, but beware that this substantially increases the attack surface. Moreover, the data sent and received is not encrypted, see Why is JSON-RPC over SSL "strongly discouraged"?.
It's recommended instead to use VPN software to set up a tunnel between the two machines. In such a setup, bitcoind will see the RPC connection as coming from localhost.