How can I get my dog to leave the cats alone?

I agree with the advice on teaching your new dog her place in the pack. While you are working on this, you may want to make extra effort to ensure that your cats have places they can go to get away from the dog such as boxes or cat trees that they can get into but the dog cannot come near. Or, if you have a multi story house, allow the cats access to one floor and bar access to this dog (or all dogs). This may be a particular comfort to your princess cat who doesn't seem interested in putting up with another puppy. As your puppy ages, she may mellow a little more, but you must step up and consistantly show her that you are the boss and you do not want her acting agressively toward the cats.