No, the pronoun "her" in the sentence "Elizabeth’s parents sent HER to boarding school in Maryland" is not a reflexive pronoun. A reflexive pronoun is used when the subject and object of a sentence are the same person or thing, typically ending in "-self" (e.g., myself, yourself, himself, herself, itself, ourselves, yourselves, themselves).
In this sentence, "her" is a personal pronoun used to refer to someone other than the subject (Elizabeth's parents sent her, referring to Elizabeth).