Hello Jarda,
DisplayLink chip and driver do not drive your mouse.
I believe you are experiencing USB communication issues, and that's why mouse stops moving and the display vanish: the dock is disconnected by the computer and reconnected.
Some of the machines now hide the some settings from the Windows 10 power plan settings (for instance PCIe ASPM, step 11 of the FAQ you linked).
Here is an utility to disable these settings to gauge impact easily:
https://synaptics.com/products/displ...ndows-lpm-tool. It also includes another executable to re-enable that later, if you wish.
Could you try and let us know if that has an impact?
Thank you,
Katarzyna