It sounds to me like you will need to pursue the fix via Ugee tablet drivers so double/triple check on that side of the issue.
It seems to me that you might need to set the Ugee tablet up as your primary monitor (as you say you've tested) so the fact that it isn't recognizing a second monitor suggests it needs to somehow be made aware of that.
I don't think this relates to your problem but...
I had an initial problem with a second monitor where I was having the mouse cursor refuse to enter that screen and I had accidentally assumed it was the screen to my (virtual) right. I then discovered it was to the left so when I moved the cursor left... my cursor appeared on the second monitor. In my case of user error... that was an easy fix. When the monitor just isn't being recognized that can be more difficult.
Good luck!