When opening multiple RDP sessions on a server (for the same credentials), the second RDP session was not able to open a Chrome window if the first session already fired up Chrome.
The problem is exactly that the two RDP sessions do not share the desktop although they are logged in with the same credentials. The desktop meaning not the "Desktop" folder but the logical entity in windows where the applications run. Therefore the instances running in both sessions can't see each other and the first one locks the profile for exclusive use which is critical to ensure no profile corruption can occur.
This problem has been discussed in the past and the best solution for this problem is to modify the startup link of Chrome to make sure every logged in user gets his own profile. this can be achieved using the --user-data-dir flag (or UserDataDir GPO policy). For example using this command line to start chrome will even guarantee that every client will reach the very same profile every time he/she logs in from the same client machine:
This will create unique folder for every user under the default profile location for Chrome. Right now there is no way to specify the client name variable in a policy therefore this particular example will work only as a command line flag.
Source: Chromium support issue #160676