According to Trinitarians, did the human Jesus worship the divine Jesus?
Trinitarians believe in the "unipersonality" of Jesus – that is, that he is one person and does not have multiple "personalities" that could interact with each other. The most important trinitarian creedal statement on the incarnation of Jesus is the Chalcedonian Definition, which reads in part:
[Christ is] acknowledged in Two Natures unconfusedly, unchangeably, indivisibly, inseparably; the difference of the Natures being in no way removed because of the Union, but rather the properties of each Nature being preserved, and (both) concurring into One Person and One Hypostasis; not as though He were parted or divided into Two Persons, but One and the Self-same Son and Only-begotten God, Word, Lord, Jesus Christ.
Thus Jesus has two natures that were united in one person. And as a single person, Jesus has one personality, as Louis Berkhof writes:
The term "person" denotes a complete substance endowed with reason, and, consequently, a responsible subject of its own actions. (ST, 3.1.3.A)
Aquinas gives the definition (following Boethius) as "an individual substance of rational nature" in his discussion of the difference between "union in nature" and "union in person" in Summa, Third Part, Question 2. As part of his defense of the idea of the unipersonality of Christ, he also states:
[The human nature of Christ] has not its own personality, because it does not exist separately, but in something more perfect, viz. in the Person of the Word. (Article 2, reply 3)
Thus, to directly answer your question: No, the "human nature" of Jesus did not worship the "divine nature" of Jesus – he is a single person.