Hmmm... I'm still not getting it.
When I'm holding the key I can't drop it if it's intersecting the door, and I can't push it if I'm not holding it. 
I managed to do it one time - by jumping in the air, releasing the key, moving to the side, and jumping again to hit the key in mid air and knock it into the door - but is that really how you're supposed to use keys?! And then I fell off the edge of the platform and the level restarted and I never managed to repeat my jumping trick. This game may be too hard, maybe? Maybe not, heaven knows I'm no hardcore gamer, but it's a shame I haven't managed to get any further because the mechanics seemed super interesting, more than many of these games (mine included).