I'm leaving this here for future readers:
The End-Solution after the analysis with Somy Ericsson was to create a second module. For the AJAX-Backend tasks i've packed my existing frontend module and this second one into a Package. The administrator module contains a helper file that response to the AJAX calls made from my frontend module's backend.
If you still want to use the frontend urls from backend, make sure to call the frontend site appropriately.
Your should use Juri::root() to get site url from administrator instead of Juri::base() or Juri::current().
Juri::root() --> http://mysite.local
Juri::base() --> http://mysite.local/administrator
Juri::current() --> http://mysite.local/...