Are you sure you understand what VPN does? This is exactly a tool used to implement of a private network on top of a public one, over the global Internet, in particular:
http://en.wikipedia.org/wiki/VPN[
^].
Do you want to use remote desktop without VPN over Internet and still be safe, it looks like you will need to develop your own analog to VPN and perhaps RDP (
http://en.wikipedia.org/wiki/Remote_Desktop_Protocol[
^]) as well. Don't forget you should probably be able to work through the firewalls, too. :-)
Care to try?
—SA