Perhaps you should look at the website Quiet Revolution, as should your daughter. Not all children are outgoing, and some like to have a smidgen of control over what they do. This is different from being outright rude and aggressive. If it is shyness and having an introvert personality in a family of extroverts, I can see her point of view. Just be quietly nice to her. Avoid, yourself and others, making fun of the way she behaves. Be accepting of her different point of view, and hopefully she will learn that she is not being treated as odd man out, and will come,out of her shell. Being forced to come to say hello, being isolated by you all as the one who is different, is not helpful for her or for the family. As for her not putting herself forward in class, not everyone is gifted with the confidence to say things in front of 30+ classmates, who may or may not be friendly.
Children who are shy are very sensitive to others underlying reaction to them. It is almost like a blow. They can see if they are sidelined, or not approved of, or that they are the 'odd man out' not as preferred as another child. Of course, some if it might be in their heads, but it is none the less powerful for that. If your granddaughter is an introvert, she will not 'grow out of it', however she may learn to live with it more gracefully if you show her that your love doesn't depend on her showing off in front of others. As you may have guessed, I was the child I described, and my grandmother was my most loved and favourite person, because I knew she loved me. She taught me to sew, and knit, both good activities for the introvert. Her love gave me a foundation to build on. The rest of my family are extroverts. I am not. This is not to say that I am a wilting flower, and obviously neither is your granddaughter. Indinana's advice as to a reaction is excellent. Just be grateful that you have such an intelligent granddaughter. Do check out Quiet Revolution though. It will help you understand.
What were the first ever records that you bought and when?
Parents-in-Law. What do/did you call them?