I agree with most everything, other than the physical contact given to “reprimand” the dog. By doing that, you may be causing your dog to think along the lines of “Hmmm…when I do something not right around that cat, I get tapped. I don’t want to be tapped I need to extinguish the cat, as the cat causes me to get tapped on the butt, which I don’t like”. What you are doing may trigger your dogs brain to realize that cat=punishment. In time, the dog will retaliate on the cat, and that isn’t what you are after. You are looking for a peaceful cohabitation between two enemies.
You want to do this in the most positive manner as possible. Any type of aversive punishment (water bottle, hitting, tapping roughly, etc.) can have the wrong effect on what you are trying to accomplish. You are setting your dog up for failure, and that is the last thing that you want. Your dog will associate the item that you are trying to make him/her like with a negative response. Let’s say that if every time you took a bite of yummy chocolate, I slapped you. You would take it for awhile, but in time you would retaliate, yell, or do something. That is what will happen to the dog.
Crate the cat and allow the dog to sniff around the crate. As you are doing this, each time the dog reacts positively (by not growling, lunging, etc.), reward the dog with a really high-value treat (chicken, steak, liver, tripe, etc.). After some time of doing this day after day for a few weels, move the cat to a room where there is more free movement and allow the dog to watch and sniff, keeping the dog on a short, tight leash. Having a baby gate up in a room and monitoring the cat on one side and the dog on the other is a great way to do it also.
Introducing a cat to a breed of dog that already has a high prey drive (it is a terrier after all) takes time, treats, a lot of praise, and a lot of patience. This is NOT something that you can RUSH. Many APBTs and other breeds never take to cats, or take to them at first, and then treat them as prey later on. Please research it more before you allow them to meet nose to nose. Always supervise them when they are together, and never leave them alone together. Many people have dogs and cats that coexist and many have grown up together, but problems still can occur. Many don’t ever get along. Just be prepared. 🙂 Cats do things that entice dogs to chase and go into hunter –> prey mode. You have to be watching them all the time!