Login iTunes / iCloud fails on Windows 10 with different user accounts

Dear community,

I have a new Windows 10 Computer with three accounts: may wife, myself (both administrator rights) and my daughter (family member).

I have installes iTunes for all three users, and iCloud for my daughter.

On my user everything is working perfect.

(also when installing iCloud on my user as a test)

When starting iTunes from my wife's or daughter's account it says "Filename already exists" (but does start).

When trying to login with the Apple ID of my wife's iTunes respectively my daughter's iTunes or iCloud both applications refuse with the error message "Authorisation failed. Operation could not be completed."

I have tried both the Windows iTunes app and standalone version, de-installed according to the different ways I found on the internet (complete uninstallation of iTunes including Bonjour etc., respectively using get-appxpackage remove), created a new local administrator user with only iCloud installed - always the same behaviour.

Logging into the web application with the different Apple IDs works fine.

Having spend several days on Google, I could not find any answer that worked for me.

Can anybody from the Community help?

Isn't that a challenge for Turingtest2? :-)

Thanks for your help.

Hunsitho