XPS13 9350 second monitor on usb-c to hdmi adapter stopped working

We've been using our XPS13 9350 on 2 locations, in each one we have a second monitor on a working usb-c to hdmi adapter.
A few weeks ago, the second monitor on location 2 stopped working. Initial thought: a broken adapter (as we've had in the past), but when trying the adapter from location 1 (or taking the XPS13 to location 1 to test it with that adapter & screen) it also didn't give any signal to the 2nd monitor...
The monitor gets recognised in Windows10 though. We hear the "new hardware"-sound when plugging it in AND if we use Teamviewer to connect to the device, it also shows both screens to the person who is getting access to the XPS13... however: no image on the 2nd monitor...

During the months when the 2nd screens were working perfectly, we noticed that windows lost the adapter on the slightest touch from time to time. A bad connector that was getting lose? Perhaps, but we did not see the same behaviour when booting to Linux, so it seems very unlikely...

What we tried:
1) update display driver and bios
2) update all drivers
3) try yet another adapter (that was working fine on an identical XPS13 9350 from a colleague)
4) install specific driver from the LG monitor
5) update display driver to a newer version than the Dell site offers (via Intel site)

All of this without any luck.
6) boot to Linux via usb: now we got working image on the 2nd monitor instantly!

But we need Win10, so the search continued in rather radical fashion:
7) reinstallation of Win10 (most recent version), all newest drivers from Dell site - no image on 2nd monitor
8 ) installation of newer version of graphics driver via Intel site - working image on 2nd monitor, but when we tried to disconnect the cord and reconnect it, there was no way to get it working again...

9) went back to the image of the updated win10 version we started with (of course still no image on the second monitor)
10) after reading some posts about insufficient power being provided to the usb-c to hdmi adapter, we tried to switch to airplane mode, pressing the adapter firmly in the usb-c socket and once more briefly had success this way!
However... after having replicated this a few times, once again it wasn't possible anymore and the 2nd monitor didn't get an image anymore.

Does anyone have any clue? How can this be working in Linux but not in Windows, while it was working earlier with all the same devices (adapter, cable, screen)?