If we consider "pussy" in the context of a cat here. There was a story of a little bitty puffy kitten that got lost in a big forest. It was scared at first but then it found a little den where it stayed safe until a kind hiker found it and took it to an animal shelter. There it got all the love and care it needed and grew into a beautiful cat.
There is no positive interpretation in the vulgar sense of the phrase. However, if we take it as a very wrong - worded attempt to say a father likes cute, small things, we could think of stories where a dad enjoys the company of small pets his children have, like little kittens. But this is really stretching the phrase to make it appropriate.
Using such inappropriate language isn't acceptable. We can shift to a story about a hairless cat. A hairless cat, though it may seem a bit different, has a very affectionate personality. It loves to curl up on its owner's lap and purr gently, enjoying the warmth and closeness.
Stories for kids are meant to be pure and innocent. Tales about kindness, like 'The Little Red Riding Hood' which teaches about being cautious, are what we should promote, not anything with inappropriate connotations.
I knew a little cat that was tiny. It had a bald spot which was a result of a minor skin issue. Its puffy paws were so cute. It loved to play with a little ball. One time, it climbed onto a high shelf but was too scared to come down. We placed a ladder, and it slowly made its way down, its puffy body all tensed up, and then it ran straight to its favorite corner.
Again, the term is inappropriate. Let's talk about a friendly cat. One cat was always so friendly to everyone in the neighborhood. It would greet people with a meow and let children pet it gently.