At one of her first royal outings without her brothers, Princess Charlotte sat tall in her chair with her hands folded demurely in her lap. Echoing her mother, Kate Middleton, she shook hands with well-wishers and listened attentively as they spoke. At 9, Charlotte, Kate’s middle child with Prince William, is becoming more of a mama’s girl. “Now that she’s getting older, she leans on her mom more,” said a royal insider. “Kate and Charlotte have such a close, cute relationship, much like Kate and her own mom, Carole.” For Kate, 42, who grew up in a middle-class British family, emulating the clo…