I have a slightly similar situation with our puppy and one of our two cats. Our female cat keeps to herself for the most part and when she does come in a room that the puppy is in she stays away from her and Zoey has learned to leave her alone for the most part. But our male cat, Rocky, likes to instigate as much as he can. He will come into the living room where Zoey is quietly sleeping or chewing her bone and rub up against her or sit right in front of her. Rocky will play with the dogs, but Zoey is still learning how to play with him. She will get too rough and he will get pissed and run away and then she chases him. I'm trying to manage this by correcting her when she chases and hoping that she learns that rough play = no play. Also hoping she starts learning from Rocky what is ok and what is not. Rocky will growl, bite and whack if neccessary. But I get irritated with Rocky because he instigates it! If he brings it on himself and bothers her, I let him deal with the consequences, unless they get dangerous. We do have a gate and our female cat will jump the gate to get in/out. Rocky is fat and lazy and will sit by it and cry until someone opens it for him....