Meanwhile i also got Portal 2 to work in “coop”-mode – very funny :-)
Anybody who doesn’t know Portal 2 yet… see here: http://www.thinkwithportals.com/.
The explanation, why the “coop”-mode first didn’t work for me: I forgot, that i’ve changed the network card configuration of the affected computer a while ago from DHCP to a fixed IP address – to temporary assign a second address to the interface. But Portal 2 wasn’t able to deal with this. After i’ve activated DHCP again and the interface only used one IP address, the “coop”-mode also worked over the internet connection.