Take a look at this thread--
I understand you're dealing with .dmg files and not External Drives, but the underlying issues both seem to be Permissions to utilize them. For me, I'm forced to completely disconnect my External Drives, shut down, boot back up & log in, and THEN reconnect each drive one at a time while entering the Password for each as they come up. I've tried deleting any saved passwords in Keychain Manager, and although I'm able to enter my Passwords successfully that time, they still fail to mount after a reboot again.
I'm wondering if this same logic could be applied to mounting .dmg files as well? You're still able to manually work around the permissions issue, just like we're able to manually mount each drive after login. Just spitballing..