Hi Ian,
Thank you for contacting Plugable! Sorry to hear of these issues.
Looking at the specs for that Alienware R12 and it looks like the USB-C ports do not support Alt-Mode for connecting displays.
The UD-ULTC4K docking station requires Alt-Mode compatibility from the host computer to use the HDMI port. I would expect the tow DisplayPort connections to work with this computer as they use DisplayLink technology that only requires USB 3.0 to connect a display.
Unfortunately there is no way to get the HDMI port for the UD-ULTC4K to work with this computer.
Please let us know if you have any questions,
Richard A
Plugable Technologies
https://plugable.com/support