Okey, I fixed it! Your last tip was pointing me in the right direction, one needs to call bind and connect in the client, and then use send. Thanks a bunch!
EDIT: Well, not quite. Bind does not seem to have much effect in the client, calling connect is the thing allowing packets to be send and recived. But, when I use it like this in different networks, it drops like 70% of all packets (I know UDP is supposed to work like this, but THAT many?), and after a few seconds, it simply dies. Since this only happens when using this on different PCs, i can't quite debug the client that way :/
Do you have any idea what could cause this?