How to get my cat to ignore my puppy?

I have a 10 month old Pom/chi and two cats that're about to turn 17.One of them, Tabitha, gets along fine with the puppy. They were even snuggling tonight. But Tigger hates her. I mean I have had to prevent her from trying to kill the dog, and she's significantly bigger than than the dog as well. The dog leaves her alone and only plays with Tabitha. Tigger will go after her just because she sees her. Tigger's been violent to the other two dogs we've had since we had her too, but they were border collies and big enough to defend themselves. Tigger used to sleep on my chest when I was little, and I'd like to buy them pet stairs to get up to my bed at night and let them in my room again but I'm afraid Tigger will hurt the puppy in the night, and Oreo has to be shut in my room at night becaue she isn't trustworthy with unsupervised run of the house, so she sleeps cuddled up to me. And I sleep so soundly I know I wouldn't wake up to separate them should a problem occur. Now that the kitties are getting up in years I really feel the pressure to make sure they don't get their feelings hurt. This has led to me sleeping in the living room with the cats so Tigger and Tabitha could sleep on me, but this is really uncomfortable and the puppy usually starts crying if I don't come to bed with her. How can I get my three to a least sleep in harmony? TIgger gets along fine with Tabitha-is there a way to convince her Oreo's a cat? Lol shes the right size