At a loss for rude and means words in 7 yo girl

What do you want her to do? What skills is she lacking that she needs? It sounds like she needs help controlling her temper and she needs help in learning to phrase things more politely.

At our house when a child is mean or rude, I immediately stop the conversation, look at them and say "that was rude. please say it more politely." If they can't come up with something, I'll give them an alternative, "You could say "I'm really mad that you dumped out my purse."" And then I'll ask them to repeat it. (Often they don't, and I don't push it usually.)

If it happens more than once, we separate the child. Yeah, it's a time out. Antisocial behavior in our house gets a time out. You are free to have strong emotions. You are free to stomp and get mad. You are not free to hit people or to say hurtful things. When you do, you clearly need some space to recenter yourself, and we're going to enforce that until you learn to do it on your own.

Once the child has calmed down a bit, then we focus on making amends.
"K felt very bad when you yelled and screamed at her. What can you do to help her feel better?"
"But she doing it wrong! She made me mad!"
"This isn't about what she was doing, this is about your behavior. You are responsible for your own behavior. You made her feel bad. How can we help her feel better?"

Then I'll brainstorm with them and try to help them implement it. Saying 'sorry' isn't the only way to help someone feel better. It could be a hug. It could be drawing a picture or writing a note. It could be fixing what we broke.

Finally, you might want to read "The Bully, The Bullied and the Bystander." It's a good book.

At school, I wonder if she can write down what she said and then work on rephrasing it more politely? So, she could be asked to write down what she said and then a better way of saying it.

I think the school stuff needs to be addressed. Have you asked her why she is talking to the teacher like this and helped her come up with a plan to stop her inappropriate yelling at school and at home. I don't think it is wrong for her to not want her stuff touched, but I do think she needs the tools to deal with her anger. My dd is an only child also and she truly doesn't think that little kids are little, she thinks they are short and rude big kids and nothing I have said to her has stopped her from this belief. I have switched my focus to how we talk to all people and to having her keep the things she doesn't want another child to touch with me. I don't think it is rude for a child to tell another child not to touch their things and I won't scold my dd for not wanting her things messed with by a destructive younger child, but yelling is rude and I do address things like that. I find that talking about how to express anger appropriately and role playing helps my dd a lot, especially when she is going through a rough patch. I think your daughter's anger at the child was very understandable, she dumped the things out of something that wasn't hers. It sounds like she got angry because her things were seriously disturbed and she didn't know how to cope with the anger without yelling. I hope the mom offered an apology for her daughter and helped clean things up.

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I know it's hard, but please, for the sake of your whole family, try to label the behavior, not the child. She is *not* mean and rude, her behavior is. The more you feel like she is a mean, rude person, even if you're not overtly telling your DD this, the more she'll feel like, well, this is who I am, so I guess I need to keep it up.

Call her on it in the moment. Don't make her admit to doing it, just tell her right then "I see you need help responding in a polite and kind way, what you can say is XYZ" She will be MAD. She will deny it, she will give excuses, she will sulk. Just continue to, as calmly as possible, model appropriate responses.

And do role-playing, "what if that gentleman there dropped his tankard onto that lady's platter, what would be a good thing for the lady to say?" "what if dogs could talk and the red dog took the yellow dog's ball, how should the red dog handle things?"

And I know there are books with second and third graders dealing with this sort of thing.

Your dd is actually lucky, I was the same way as a kid, but in me it came out as crying so I never got proper help dealing with my belief that I knew the One True Way and that everyone else was trying to annoy me when they did things wrong, er, differently.

Like with the 3 year old dropping things from the purse, it wouldn't have been an accident it would have been the 3 year old deliberately messing up my things.

Having a toddler has done wonders for these feelings. But since you can see the anger directly, you'll be able to help your dd get through this far sooner than it has been happening for me.