Do both games list the version as 2.0.119.430 in the main menu (below the column of buttons in the keyboard UI, top right in the controller UI)?
The initial update to add Galaxy support to the GOG version had a compatibility issue playing co-op with either Steam or the pre-Galaxy GOG version, so your girlfriend should be using the 'GALAXY FIX' or the more recent 'LAN HOTFIX' (for the Czech localization), or the version before the Galaxy update. By default it should have updated if she is using the Galaxy client, but if she downloaded the full installer the weekend the initial Galaxy update was released, it may not be up to date (there is a patch).
If your girlfriend is using the Galaxy client, she can try reverting to the pre-Galaxy support update (select the game in the left column, click More and select settings, switch the update to manual, then select 2.0.119.430 rather than 2.0.119.430(LANG HOTFIX) ).
Try the Direct Connection using an IP address, or LAN if possible (if the computers are not on the same local network, you'd have to use VPN software like Hamachi or Freelan).
