My guess is that people know, but your description was lacking the necessary detail to give a usable answer.

About packets being sent to the wrong link, what does 'ip route', or 'route' display? My gateway shows something like

irus:~# ip route
128.2.x.x dev ppp0 proto kernel scope link src 128.2.y.y
10.0.0.0/8 dev eth0 proto kernel scope link src 10.10.10.10
default via 128.2.x.x dev ppp0

In your case the ppp0 would probably be eth0.

As far as remotely starting apps that connect with the 'local' Xserver, it depends on. Do you already have an X server running on the machine? If so what user is running it and if it is a different user you probably need to pull the right authentication information out of the ~user/.Xauthority file. (I typically just copy it). If X isn't running yet, you can probably just start the server with startx.

Once X is running on the server, and your userid has the right cookies to connect to it through copying the Xauthority file (or extracted/merged with xauth), you can simply set the DISPLAY environment variable to :0.

f.i. 'env DISPLAY=:0 xine'