Can you try setting the IP address of the Coordinator instead of the host name in the agent’s settings?
Another thing you could try is to change the NIC priority in the Windows network settings, so that the internal connection becomes the default adapter.
The Swarm Agent creates a number of sockets, and I’m not sure which one is used for what purpose. It looks like the local listener socket might just bind to localhost (127.0.0.1), which on Windows translates to the default network adapter (on all other operating systems this would bind to all available adapters, but Microsoft is cooking their own soup). I don’t see a way right now to override this behavior for multi-homed computers, but it shouldn’t be too hard to make it configurable and expose it in the Settings UI. We are planning to rewrite Swarm in C++ later this year or early next year, so I don’t think that we’ll be making any changes to the C# version on our end (unless it’s a critical bug).