Years ago we installed a cat door in our bedroom door to allow the cats some mobility while preserving a bit of privacy for us. We found that not all cats are smart enough to learn how to use it. More on that later.
When we brought Arnold and Cleo into our home we found, to our dismay, that Fervor would viciously attack Cleo. A solution that has worked reasonably well is to keep Cleo closed in our bedroom when Fervor is out. Then we separate Fervor for a time to let Cleo have the run of the house. Getting this method to work when we have visitors is quite a challenge.
Arnold quickly learned how to use the cat door but Cleo does not use it. For a while Fervor did not use it but one day he went through it and tangled with Cleo in our bedroom. Then I glued little wooden blocks on the inside of the cat door frame to allow only exits from the bedroom and thereby refuse entry to Fervor. When Fervor has the run of the house, many times he sits outside the bedroom door staring at the cat door as in the photo, above. We call it "watching TV" as he can see shadows through it. He is waiting for Cleo to come out (she never does) so he could pounce on her.
The one-way cat door allows Arnold to leave the room when he wants. Arnold is apparently a very smart cat. He can open the one-way door from the outside, pulling it toward himself, and enter the bedroom. This is great but if Fervor every learns to do that (doubtful) we will have to lock the cat door closed for all.
One last thing. The broom standing next to the door is intended to be used to separate Fervor from Cleo if they should ever engage. We have several such "cat brooms" placed around the house as defensive measures.