I had sort of the same issue with my yorkie and my cat. My yorkie would go after my cat. What i used to do is everytime this happened, I would put Duchess in the powder room. She hated being in the powder room so after a few times of doing this she gradually stopped going after the cat. However I nipped this in the bud from the very start so it didn't take her as long to stopped her from doing it.
However the cat was extremely smart. She use to pick a fight with Duchess and and of course I would put Duchess in time out not realizing it was the cat starting it.
I actually saw the cat take a few swats and Duchess, Duchess would get excited and start barking while the cat would jump up to some placehigh place looking down on Duchess and thinking "what an idiot". Anybody who has cats knows how they can sometimes be jerks. All this time I thought it was Duchess.....mean evil cat plotting ways to get rid of Duchess