Am i in the wrong?

for some context i am a 16 year old girl. I used to live in a different state. Most of my family lives in my old state, so every 2 or so months, i like to go back to visit them. My brother and i are the ones who do so as my parents have work, so we just go alone and live with my cousins. I have a large extended family, including 17 aunts and Uncles and countless more cousins. Most of my cousins are all older than my brother and I. So we dont really have a lot in common. My second oldest cousin, has 2 daughters, (9 and 6 respecitvely) and i live with her for the duration of my visit. I love my 2 little nieces so much and i adore all the time i spend with them. Because im very close with them, i always bring them gifts while i visit. My cousin doesnt speak english very well and is a bit unfarmiliar with things, so during our stay, my brother and i always go pick up our nieces from school. 

One particular day, when we went to pick up my oldest niece, call her ava, she was obviously sad. not crying, but sad. I asked her why and she wouldn't tell me. After a while, she caved and told me this:

A girl, say her name is zoe, was picking on ava during lunch because ava's food "smelled bad". And this had been going on for a while. Every day, my cousin pack ava some sort of aisan food for lunch as thats the only thing she knows how to make. Ava's lunch mainly consisted of a small side dish of japanese seeweed salad or kimchi or bamboo shoots. The main, being something like fried rice, noodles or stir fry. And some aisan snacks. And this Zoe girl was complaing about how bad the food smelled. 

Hearing this, i was kind of mad. So i asked ava to take me to see this zoe girl while my brother stayed in the car. We found zoe in the playground and i kindly tapped her on the shoulder. Now i wanst palning on lecturing a 9 yr old, but reminding her that is was wrong, but boy this kid was rude. first thing she did was say "hellaur?" very rhetorically and when i introduced myself, she laughed. 

Me: im ava's - 

Zoe: ahhahaha ava? Whats wrong

Me: well i wanted to remid you it is very rude to bully other students based on what the ea-

Zoe: eat? yeah i know. 

me: huh?

Zoe: lady, im KOREAN. and today ava had kimchi. I dont know where she got that kimchi but its stinky. And definetly not real Kimchi. and i think thats a bit rude.

Before i could speak, Zoe's frickin mother lunged at us and joined this conversation:

Mother: well i think its a bit rude your engaging in such conversation with a little girl dont you thinkg? are you avas mother?

Me: im sorry but i -

Mother: Wow! a teen parent! no wonder! you need to better educated ava! Its not cultraly apropriate to be eating kimchi at school. Esspesially for us Koreans.

And then her mum just left saying " zoe dear, 15 more minutes of playing then we go"

I was just so sick of being interupted by this mother daughter duo so i straight up yelled at zoe. 

i might of went a little bit overboard but to defend my niece, ill do it again. Well zoe broke into tears and ava and i left. The next day ava got in trouble with her teacher and parents were contacted. I arrived with my cousin to defend ava and apparently ava was suspended! SUSPENDED! a 9 year old. I cant help but think its cuz of what i said and none of this wouldnve happened if i just let it slide. Am i in the wrong?