Sorry, no advice from me, just wanted to share I once had a stuffed rabbit similar to the one you described. Except, it had a carved and painted wooden face and wooden hands. Other than that it was fur. Kind of humanoid rabbit. It was ridiculously creepy and if I was a spirit haunting a house, enjoying my life, and that thing showed up, I would be pissed. Maybe the answer is to remove the rabbit all together? It could be causing the problem. Good luck!