I'm only a lurker here, but I found a possible solution/workaround for anyone else who is having trouble with the fishing mini-game to grab Harley's room key. This worked for me so hopefully it can help other players too.
So when you're in the Harley bathtub animation/mini-game you can use your keyboard for alternative controls. Use the 'a' or 'd' key to select the hole to your left or your right. You should see the hole highlighted, slightly whiter than the other holes.
Once you've selected the hole you want, press the spacebar ONLY ONCE, to lower the fishing line. Press the space bar again to raise the fishing line if Harley is looking/isn't moving her leg. DON'T HOLD THE SPACEBAR, it just becomes stuck in an up/down animation. Once the fishing line makes contact with an item bubble it will automatically pull it up for you. Hope this helps someone.