This is exactly the sort of situation that network swiches (hubs) were designed for.
In theory, it would be nice to think that your DS pc should be able to simultaneously communicate with both the modem and the US pc, but in reality this won't work (unless the motherboard has two network ports and is specifically designed to do it). You are trying to use your PC as a hub and it isn't designed to work that way. The problem occurs because your pc only has one IP address, but two ports.
You should be able to pick up a cheap 4-way switched hub on an auction site for a few quid.
You can either use a modem plugged into the network switch (via the network cable) or the other way to do it is to use a router which combines the two devices into one box.