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my previous comment just works during the time of the installation. When your Mac boots on the new system on the new drive it will see the 2nd physical hard drive and automatically mount its partition.
you mean, make the other drive invisible while you install your 2nd system ? Yes, go to the Utilities menu when you've booted on the OSX install volume, open Disk Utility, select the volume you want to hide and click on the "unmount" button. Quit Disk Utility, the Installer will only see one volume.
Could you create a new user account on the Mac and try to launch Google Chrome from there ? It will help to determine if the issue is within your usual user account or system-wide.