Mapped domain only showing whe I am logged in?!

Ok. Where to start… here to start:

For some funny (not really) reason the domain that I want mapped appears to be in the right spot, showing the subsite I set up to try it out.

BUT only when I am logged in. I have been chatting for hours with the support team at my host and they cannot resolve it as it seems to be a plugin/wp issue.

PLEASE help me. I am going crazy over this!