When the AJAX Remote is enabled, the HTTP server in Remote Buddy 
accepts connections from all network interfaces, including Ethernet. 
It is not limited to WiFi connections. Like any other HTTP server (for 
example the copy of Apache included with OS X), it can be accessed 
from outside if you set up the network accordingly.

I'm sorry to say, but I can't help you with the setup/debugging of 
your network, VPN, Firewall or router, though.

Best regards, 
Felix Schwarz