Last we heard about Caia Howcroft, the Princeton fifth-grader was appearing in “A Midsummer Night’s Dream” with the New York City Ballet. This month, Caia is back on stage in “George Balanchine’s The Nutcracker,” alternating as a mouse and, shown here backstage, a “polichinelle.” Caia is especially pleased when the Sugar Plum Fairy is played by fellow Princeton native Unity Phelan, who goes out of her way to high-five the dancers after performances and tell them they have done a good job.