I think you did the right thing too and handled it the right way. It must have broken your heart, it made me feel awful just reading your thread title. You poor thing

I think it's really important too to sit her down and explain that "hate" is a very strong word and can really hurt people and it's not a word that can be used lightly. How to explain that to a 3 year old, im not sure. But im sure you will find a way

Good Luck!