When I deactivate the SEF, the login screen stays on the default page (which is better than before as i used to go to another empty screen with login fields only). However, after logging in, I do not go to the control panel but to the joomla user data profile screen (same as before).
So, to solve my problem, here is the compromise I reached. I created a login module on the hikashop page and set the url redirection at login to the hidden menu page for the user control panel and set the url redirection at logout to the main hikashop page. Because joomla gives you access to write in the exact urls for login and logout, I was able to attach this feature (user control panel). Otherwise, it does not work from inside hikashop.