With SSH you can redirect the GUI of some remote command to your local desktop, but it will not show simultaneously on the remote machine.

In order to do what you want you will have to use some kind of proxy application able to connect to both X-servers and send the X commands to both. I don't know if such application exists.

Another option would be to use x11vnc to access the remote desktop via VNC. But, IIRC, x11vnc will not transfer video to the remote side, you will see a black box instead.

update: see XMX.