I have several computers on the same network. When I am on the network (internally) I access the machine I want via it's IP address or computer name all are on the default port (4899). If I am outside the network, accessing from the internet I have set the router set so that the incoming (external) port resolves to the specific machine IP/name and the default port (4899).
Example: Radmin connects from the outside using the "public" port 4895. The router sees that and directs to 192.168.x.x and the "private" port 4899.
You should have a router that will direct the Radmin connection depending the port you use from the outside. you need to configure Radmin, lets say on a laptop that you will ust to connect via the internet to your network. If your network does not have a static IP address then you would need to use a service like DynDns.com, which will keep track of the IP address of your ISP network connection via a small program that would run on one of the computers inside your network.
For each computer you want to access you need to have the Radmin Server running. On your laptop you would configure a connection for each computer using your network IP (or DynDns DNS name)and use a different port number for each. Like computer 1 is port 4899 and computer 2 is 4898 etc. On your router you access the setup program and configure the "Virtual Server " so that when the router sees a Radmin connection on the 4899 public port it is routed to 4899 private port at your computer 1 IP address, and a Radmin connection on the 4898 public port it is routed to 4899 private port at your computer 2 IP address.
If you are not familiar with the routing sertp let me know what router you have and I will try to assist.