Try using xdg-open. This will open the site in the currently registered application for URIs on the remote linux system. If the browser is not already open, it will start it. If the application is already running, it will open a new tab (if the application allows it). Since you are using the remote display in the OP (
export DISPLAY=:0) this will cause page to open there (again, as long as midori is your default browser - which you can check with
For more info on xdg-open, look here.
If, on the other hand, you are really wanting a remote-control style solution, without the extra weight of an RDP or TeamViewer style options, consider using something that allows a local XWin server (such as Cygwin does for Windows hosts, or already available in any linux system) for your SSH connection. Then all you will need to do is connect with
-X in your ssh command and the application gui will arrive on your local system, but be running on the remote. In this way you will not need all the extra desktop stuff.