Well ok now I understand why it wasn't working.
I was indeed attacking Nelly, but I never fled and went back to the room with the bondage horse. I went there once after getting the key, but I thought it was just so you could know what the key was for. In the main room, there is another bondage horse (right by the bottom door, if I remember correctly), so I thought you were able to tie her up in that room with it. :/
Edit : just tried, it worked this time ! Thanks for the tip.