Hi, I have a barn door at a T-intersection hallway in my house (see photo). I installed this because one of our cats is mean to our other cat. Unfortunately, the smaller bully cat is also very smart and has learned to open the door-it can open regular doors too. I would like to install a double sided latch or lock so the cat can't (at least I hope) open the door. Usually they are not in the house togther accept at night. Thanks.