How to connect from localhost-router-Internet-router-localhost Port 3456?

Assume I have an successful working in-house LAN with a router which works as well as gateway to the internet.

Now I want to test how a client on my local computer works with a server on my local computer.

When I connect both directly on my machine then everything works fine.

However I want to find out if they cooperate as well if they are connected through the Internet.
In such a case possible difficulties regarding Firewall, NAT port forwarding, DNS lookup
and others would be detected.

How can a simulate such an routing over the Internet? How can I force my local computer
not to take the easy, direct way but to redirect all TCP/IP packets through the internet?

Using a Proy somewhere in the world would not work because proxies do only work for port 80
and http protocol.

How can I achieve a similar routing for lets say communication over port 3456?

Ken