Relationships

My daughter, who is nine years old, has a habit of putting people down. She has a six years old sister and a three years old brother. She has the feeling that she needs to be and show superiority. Is it because she doesn’t feel good enough?
When I see her impatient with her siblings, should I take her with me or to the calm-down spot and help her calm down? Walking away from the situation for a little bit helps her best. The calm-down spots help her too.
I feel like I cannot do “group problem-solving” because it happens too often. What type of reminder should I do for her?
Also, she gets irritated and annoyed with people very quickly. It is something that my husband does as well. Being impatient, stopping people when they talk or talking on top of them, raising their voices, and walking away in the middle of a conversation.
How do I explain the benefits of keeping a positive and pleasant relationship? What are her responsibilities in maintaining good relationships?
Please share more information about relationships, and if you can recommend any books or resources, I would appreciate it very much.
How do I help her break the habit of looking down on people? Or am I missing something more substantial?
Thank you very much!