Hi Ed, thanks so much for your help. It works now.
So the solution for everyone hosting their one wordpress site on multiple domains (for example to have 2 different languages) and experiencing the described problems above. As Ed found out to enable CORS.
Here is how to do this on a Apache Web Server.
In the .htaccess file of your wordpress installation root ad the following block
<FilesMatch ".(ttf|otf|eot|woff)$">
<IfModule mod_headers.c>
Header set Access-Control-Allow-Origin "*"
</IfModule>
</FilesMatch>
Be sure mod.headers is enabled on your Apache. If you want to get sure shh your server with
a2enmod headers
and restart Apache to activate.
sudo service apache2 reload
Information about enabling CORS on other server environments can be found at
http://enable-cors.org/server.html
Have fun!
Florian