Just a quick drawing of the first meeting between Zap Apple and her dog Winona IV.
After the incident with the timberwolves that resulted in half of Zap's front leg having to be amputated, Zap developed a strong phobia of dogs and would panic even when seeing the farm's dogs whom she had grown up with. And since the Apple family prioritized Zap's mental health over their dogs, Winona III and the rest of the farm-dogs had to go live with Fluttershy.
While they made sure to never complain about this, Zap could see that her family missed having them around: both to help with work, and also just because they liked dogs. They could visit, but it wasn't the same. So without telling them (since she knew they would feel bad and not want to pressure her) she asked Fluttershy for help getting over her phobia. She ddn't need to like dogs, she said, just not be afraid of them.
This was very well timed, as Winona III was pregnant and Fluttershy decided to try and help Zap by having her come over and meet the puppies as soon as they were born. This worked out suprisingly well, as Zap found that newborn puppies didn't really look or behave like adult dogs. She was still afraid, but she was able to be in the same room as them and eventually even worked up the nerve to pet one of them, all without panicking too much.
Right after this scene, Fluttershy pretty much went "K, you watch her while I go talk to her mom" and dropped her in Zap Apple's lap. Zap was paralyzed for a while, before realizing that the thing in her lap couldn't even see… or move, since it appeared stuck on it's back, wriggling it's little pink paws uselessly in the air. When Fluttershy came back, Zap was a bit upset, but didn't say anything because it would wake the pup sleeping on her tail.
Zap visited pretty much every day, and as the puppy got older Zap got more and more used to her looking more and more like a dog. She also calmed down around the other dogs as well, until she was even able to pet them without tensing up; she still didn't like them, but it was fine. The puppy though, who at this point was pretty much a dog, she was completely enamoured with, deciding to keep her as a pet and named her Winona IV.
The dogs could return to Sweet Apple Acres, everyone was happy and it seemed like the plan had worked. …Until a stranger dog came by and barked once, sending Zap up into a tree until Winona IV chased it away. Turnes out she didn't cure her phobia of dogs, as much as she made the farm-dogs an exception to it.
She decided that it is fine for now; she has Winona IV to keep away any strange dogs from her.