In this situation it could happen that you double click the chrome icon on the desktop and nothing happens.
I tried to search the internet about this problem and find this (useful) link
The problem depends on the fact that we are using the same profile data on several sessions (more or less) and the solution is to launch chrome with several command line parameters.
So I have putted this line:
chrome.exe --user-data-dir=%LOCALAPPDATA%\Google\Chrome\%CLIENTNAME%in a .bat file and created a shortcut on the desktop for it.
Hope it can be useful to someone else!