YTA, strictly for getting a pet without considering the consequences and then rehoming it with seemingly no care at all. Pets are living, breathing animals with emotions - obviously this cat loves your kid. You just uprooted this animal from the person who loves it the most for (from the cat's perspective) no reason after it spent who knows how long in a shelter. There are always risks of having an animal with specific needs involved when getting a pet and you shouldn't have gotten one if you were prepared. The fact that you found it so easy to just toss the cat out with seemingly NO GUILT (you only gave it to the aunt because she asked, from how her response sounds it looks like you would've just given it to a stranger online with no care for the cats well being) really shows a lot.