Problem with language

Hello
I am not sure if my questions have reached you, so I will try again.
Here is the problem:

I have set up my website in two languages German and English. Everything works fine, if I'm not logged in.

However, if I log in, only one langrage will work. Either the German Toolbar or the English. It depends on how standard language in Joomla is set - German or English.

I found out when I set the default language to English in Joomla
I see the English toolbar in my website.

http://prntscr.com/luarp5
http://prntscr.com/luar04

If I set the default language in Joomla to "German" I only see the German toolbar
http://prntscr.com/luarb5
I think that the Templers have installed correctly
http://prntscr.com/luas3o

The menu structure seems to be correct
http://prntscr.com/luasg9

To make it easier the logos in toolbar show German or English. As you my see the do not switch properly by clicking the flags. So please try both ways – log yourself in in front end and vice versa do not log in. You will see the difference.

Thanks for any help