When going to the basement doors and triggering the cutscene where the halfling gives you the key, you then have to face the doors and open them with the key.

However, the interaction point for both doors there appears to be on the OPPOSITE side of the door, making it a huge pain in the ass to actually use the interaction point. :-s

Depending on where you stand when the cutscene is triggered and you'll finally get the key, you can be very near the door.
When I first turned around after I got the key, I had been almost touching the door.
For me in this situation it helped to move a few steps up (away from the door).
When I returned I could open the door, no problems.

For me, they didn't appear at all to start; in that instance I'd been right next to the doors.... cutscene doesn't start till that point.
In the scond instance, I ran back up stairs and back down and then moved around a bit, but they were still only accessible from one very odd angle for each door... hence my suspicion that they are spawning behind it.