Terje, this sounds like an exciting project. I think eZ publish will fit well with your needs. It's easy to build hierarchies and relations with eZ publish.
Would be nice to get information about the project once you start progressing with it.
While the TNG license is "almost" free ($27), PhpGedView is another genealogy program that is GPL licensed. PhpGedView is similar web oriented and can typical run on LAMP or WAMP servers: http://phpgedview.sourceforge.net/
There is also similar developed module files to integrate phpGedView with PostNuke. http://phpgedview.sourceforge.net/modules.php
It is similar wishible to run these programs as modules under eZ publish, without the need to login extra to the genealogy programs.
Is there some kind of documentation and command examples for eZ publish how to do this?
there is information about how to write a module and how to connect to the user information in eZ publish (login handlers). There is both a tutorial on how to write a module and information on how you can write your own login handler.
You can find this under the eZ publish documentation.