After dancing around her front garden like a swan again, she "takes off" and we get her POV as a metaphorical (?) swan flying over the stunning Irish greenery, before we cut to a plane and then Rosemary is in New York with Anthony's American cousin Adam.
He takes her to see Swan Lake, and she imagines herself as a child dancing on the stage. At dinner, he suggests he maybe wants to propose to her, and she says she hasn't given up on her childhood dream yet (that'd be Anthony getting over himself and asking her out). They kiss anyway, and Rosemary heads back to Ireland. After one entire day in New York.
Her flying to New York for one day is, like, only the 10th most insane thing that happens in this movie.