In Trinitarian theologies, which nature is subservient to the Father?

Question

In Trinitarian theology, when Jesus uttered the following words that indicate his subservience to the Father, which nature was Jesus "accessing" / "operating in": his divine nature, or his human nature?

• John 5:19:

  So Jesus said to them, “Truly, truly, I say to you, the Son can do nothing of his own accord, but only what he sees the Father doing. For whatever the Father does, that the Son does likewise.

• John 14:28:

  You heard me say to you, ‘I am going away, and I will come to you.’ If you loved me, you would have rejoiced, because I am going to the Father, for the Father is greater than I.

• Luke 22:41-42:

  And he withdrew from them about a stone's throw, and knelt down and prayed, saying, “Father, if you are willing, remove this cup from me. Nevertheless, not my will, but yours, be done.”

Excerpt from Henry Bettenson's English translation of the AD 451 Chalcedon Formula:

...

and at the same time of one substance with us as regards his manhood; like us in all respects, apart from sin; as regards his Godhead, begotten of the Father before the ages, but yet as regards his manhood begotten, for us men and for our salvation, of Mary the Virgin, the Godbearer; one and the same Christ, Son, Lord, Only-begotten, recognized in two natures, without confusion, without change, without division, without separation; the distinction of natures being in no way annulled by the union, but rather the characteristics of each nature being preserved and coming together to form one person and subsistence, not as parted or separated into two persons, but one and the same Son and Only-begotten God the Word, Lord Jesus Christ

I borrowed the language "operate in his divine/human nature" from Eleonore Stump's explanation of Jesus as God (min. 5:40-5:55).

To me, especially from dythelitism perspective where each nature has a distinct will, it makes more sense that in the 3 verses above Jesus operated in his human nature, whose divine nature communicated His will, just as we discerned God's will for us. Because if Jesus was operating in his divine nature, in order for these 3 verses to have any real meaning of subservience, how can one being has two potentially conflicting wills?

If there are major camps representing different answers, I'll edit this question to add a comparative-christianity tag.

Answer 1

Specifically, it is not the nature but the person who acts. Christ has two natures, human and divine, and His actions and statements are ascribed to either one nature or the other. In John 5:19 Christ is referring to the one divine will, which He possesses by divine nature. The statements in John 14:28 and Luke 22:41-42 are ascribed to His human nature and will.

Answer 2

The answer to the "My Father is greater than I" part of your question is given in the so-called Athanasian Creed, printed in copies of the 1662 Anglican Book of Common Prayer.

This declares that our Lord Jesus Christ is

"God, of the Substance of the Father, begotten before the worlds; and Man, of the substance of his Mother, born in the world. Perfect God and Perfect Man; of a reasonable soul and human flesh subsisting. Equal to the Father as touching his Godhead; and inferior to the Father as touching his Manhood." ...

That last clause is the answer to "Why does Jesus say 'My Father is greater than I'?"

However, I suggest that the whole Person of Christ takes part in the obedience evident in the other two quotations, because I regard even the event of Incarnation as part of that obedience. In the matter of judging the world and giving life, which is the topic of the John 5 passage, John's point is that the Son coordinates his will with that of the Father, so that there is no difference between "He judges" and "I judge".