Remote Desktop between two linux clients.

use

ssh -X username@remotesystem

then run the gui application

try this 2 article
i might help you


you need to install vnc server
https://www.experts-exchange.com/questions/22900438/Redhat-Linux-Enterprise-unable-to-access-via-Remote-Desktop-but-can-ping-SSH-etc.html

and also

http://www.linglom.com/2008/02/11/enable-remote-desktop-on-linux-using-vnc/

The ssh would work if I only wanted one application, but I want the full logon prompt would the VNC solution give me this?

if you want full desktop of another linux pc then you need to instal Vnc server, check those article you should be able to understand

Use rpm or yum to install vnc-server and then put entries in the /etc/sysconfig/vncservers file.  That will allow you to have vnc server sessions started at boot time.  Typically you would put in a few, like:

VNCSERVERS="1:user0 2:user1 3:user2"

Use a client to connect to port 5901 for user0 desktop, 5902 for user1 desktop and 5902 for user2 desktop.  You need to run vncpasswd as each user to set the password for each vnc user.  

You may also need to edit the xstartup file for each account.  the file is located under the users home directory/.vnc/xstartup

The contents should be something like this:

unset SESSION_MANAGER
exec /etc/X11/xinit/xinitrc

[ -x /etc/vnc/xstartup ] && exec /etc/vnc/xstartup
[ -r $HOME/.Xresources ] && xrdb $HOME/.Xresources
xsetroot -solid grey
vncconfig -iconic &
xterm -geometry 80x24+10+10 -ls -title "$VNCDESKTOP Desktop" &
twm &


At that point you can use the vnc client from one machine to the other.