I got it. Both me and my son choosen stay offline. We set names of our characters. But probably under the hood there is something like a 'player name'. After registering my account and going offline, this was probably overriden, so my son could join my game even though he was still offline.

So most probably the joining player was always kicked because he has the same player name as the host. I could not find where I could change my player name while being offline.

I've read that Neocore has taken down the online servers so registering an account may not be an option any longer.

Is there any other way around this bug that prevents multiplayer over LAN?

I know this is a bit late, but in case it helps anyone else - I had the exact same issue, and here is how I got it working:

The problem: This was caused by my partner and I both being logged into the same GOG Galaxy account on each of our computers, and - I'm guessing to make the "Friend list" feature work - the game uses Galaxy to lookup the user id, which then ended up being the same for the both of us. Using Cheat Engine to inspect the game, I could find `poacher2k` and my unique GOG ID (a long unique number) being in the game memory, and I also saw what looked like requests being made to GOG, so this theory seems pretty sound to me.

The solution: Either logout / uninstall galaxy on 1 of your computers (or more if you're playing 3-4 players), or go to `C:\ProgramData\GOG.com\Galaxy\redists` (your path might vary) and rename `GalaxyCommunication.exe` to something like `GalaxyCommunication2.exe`. The game won't be able to find the program, causing the user lookup to fail, and you'll be able to play just fine.

You might also need to end the "GalaxyCommunicationService (32-bit)" in Task Manager if it's already running.

Hope this helps!

Edit:
I don't think this matters, and I'm not sure what it's for, but you can also change the `ProfileName 0` string in `regedit` at `HKEY_CURRENT_USER\Software\NeoCore Games\Van Helsing Final Cut\Options` to something other than `Offline`, which is the default. If you have Galaxy installed, you still probably need to do the above though.