AITA for standing my ground?

My sister(X)(33F) and I(23F) have had a distant relationship for most of my life. Earlier this summer, her kids stayed over at my parent's(AB) house. During the entire two weeks they were there, the youngest(Y) antagonized AB, me and their sibling. Because X wants to raise her children differently from my AB(I don't have an issue with this), we have to talk the kids through their emotions and aren't allowed to punish them traditionally. This didn't help, as Y yelled every time something slighted them, didn't get their way, etc.We tried to talk to Y, threatened to call X and her husband, and took away going places. AB didn't want to ruin their time so they gave in often, and didn't want to bother X. Eventually, the day they were leaving came. I had to drive 16 hours the next day so I wanted some good sleep. But like every single day for the past two weeks, they again woke me up early screaming. I got up and went to ask what was going on, and Y flipped. Y talked down to me, was blatantly disrespectful, and hit me. I had it. I yelled Y was a 'dumb little brat', slammed the door, and went to bed.The next day, I found out from my mother that X was angry with me. I asked and she said X wanted me to apologize for calling her child a "dumb little brat". I explained why I thought that was dumb, considering how Y had treated everyone. Y WAS being a brat. After about two weeks of not talking to X about the situation (we don't talk normally because we aren't that close), I finally decided to text her. I explained while I understood it was rather rude to call a child a name, it was out of anger for the way Y acted and nothing more. I don't think Y should get a pass for their behavior just because they were a kid. She kept explaining that Y was a kid, and kids are emotional and act how they act, Y's still learning self control, etc. I thought that apologizing would teach Y nothing and they would continue to act out.We went our separate ways and that was that, or so I thought. She refuses to talk to or about me. AB want me to apologize for the family's sake, but don't force it. Recently though, X texted me and said she is removing me off of the family(AB, her and her husband and me) phone plan. Now if there were any other reason for this, I really wouldn't see an issue. But it costs everyone money to remove me from the plan(it gets cheaper the more people you add onto the plan). I'm not worried about the money, but I feel like she's going too far for me calling her kid a brat. I want to forget about this whole thing and move on. I'm still buying her and her family gifts for Christmas, birthdays, etc and I haven't treated her any differently.Is this behavior justified? I know an adult calling a kid a mean name is rude, so I understand if I'm the asshole on that. But is me continuing to stand my ground on such a small issue really worthy of how cold she's being? It's been months. Should I really have just apologized? via /r/AmItheAsshole https://ift.tt/2GvYViY