Ouyang, which is the head and which the complement in "I want her to look like a princess"?
I would say there are three complements in the sentence. The phrase (or non-finite clause) "her to look like a princess" is the object of "want". So, it's a verb complement.
Head = "want" / Complement = "her to look like a princess"
The phrase "to look like a princess" is a verbal complement of the object "her"
Head = "her" / Complement = "to look like a princess"
The phrase "like a princess" is a predicate adjective of a linking verb phrase, but I wouldn't call it a subject complement because "her" is not in the subjective (nominative) case. Perhaps it is an object complement.
Head = "her" / Complement = "like a princess" ?
It's kind of like the predicate adjective in the verbal phrase "Being completely honest is the best policy". What is the noun that the adjective "honest" is modifying? Subject complements don't complete subjects in the way that other complements complete the heads of phrases. Subject complements actually complete verb phrases. We understand the meaning of the subject perfectly well in linking clauses. It's the meaning of the verb which is completed.
Compare subject complements with a prepositional phrase complement of a subject. If I use an indefinite pronoun as a subject without an antecedent, "None make sense", I must add a complement to complete its meaning "None of his ideas make sense". So, I wouldn't disagree with classifying linking verbs as the heads of subject complements in both finite and non-finite clauses.
Head = "to look" / Complement = "like a princess"