Thank you for the clarification.
Perhaps the tutorials and information on the internet misrepresent this setup. But it seemed like it worked for other people, xinerama connects the two screens and RANDR advertises the 2 "physical" outputs.
I tried to use disabled xinerama
Xephyr -screen 960x540+0+0 -screen 960x540+960+0 +extension RANDR -xinerama :1 &
but that also doesn't do what I want (xrandr sees only one output and the xterm cannot be moved between displays), even though
DISPLAY=:1.1 xterm &
now works.
What I want is to mimic a 2 monitor setup, i.e.
DISPLAY=:1 xrandr
to show 2 outputs as if there were 2 monitors.
Xinerama might be still necessary though for the WM to see the whole Screen to manage. The terminology of "screen", "output" and "display" is used somewhat inconsistently it seems to me.