When I was reading Hawkeye #18, I was initially surprised that Kate would do something so stupid as bring a cat used to living in its own home, into a trailer that was the home of another cat and a dog. And that she would then be surprised that didn't work at all.
But I hear enough horror stories from my dad and my coworkers to know most people don't have a damn clue what they're doing with pets. I sort of get it. Kate likes Harold's cat - or she likes Harold so she agrees to look after his cat, close enough - and she likes the old ladies whose cat she's watching, and she likes Pizza Dog. So since she likes all of them, they will all like each other, right?
Hahahahahahahahahah - No. But that's Kate. She's endlessly confident in herself, and eager to help people. The problem during her stint in L.A. is that she keeps butting up against the limits of her experience, be it with pets, or at being a detective. She doesn't understand the risks in bringing a new animal in another one's territory, just like she doesn't really understand how to deal with one brother releasing the other's music, or a wealthy weed dealer stealing an orchid. Shooting arrows really well only works if she can find the right place to put the arrow, and she's had only limited success with that. She's a quick study - witness her learning some things about archery by watching Clint once - but she doesn't have anyone to teach her how to be a shamus. Harold was offering supportive platitudes, but not much practical help. The cop is too busy trying to dissuade her before she gives him an ulcer.
I'm honestly surprised the Old Ladies Cat and Pizza Dog got along, with Kate bringing the dog into the cat's domain. That is a remarkably reasonable cat (I'd question the Old Ladies.letting this unknown girl with a dog watch their trailer and their cat, but I guess they were desperate).
I do wonder if it's significant that Kate tried taking the cat back. Admission of defeat? I don't know. It got her the real scoop on Harold, but her attempt to help him failed utterly. So she's struggling with the limits of what she can accomplish alone, after she got fed up with Clint being mopey and trying to do it all himself.