A claim about the incarnate Son—particularly a claim about the relationship of the incarnate Son to the Father—may be a trinitarian proposition, but it may also be a christological assertion. To take a classic example, well worked through in patristic thought, when we hear Jesus pray, either in Gethsemane or in the high-priestly prayer of John 17, we necessarily hear the authentically human voice of the incarnate Son pleading with God, not an internal triune dialogue between the eternal Father and the eternal Son. [Stephen R. Holmes, "Classical Trinity: Evangelical Perspective," in Jason S. Sexton and Stanley N. Gundry, eds., Two Views on the Doctrine of the Trinity (Grand Rapids, MI: Zondervan, 2014), 44]
When Jesus prays to the Father, is it an intra-Trinity dialogue? According to Holmes, who claims the support of the Church Fathers, it is the human voice of Jesus praying to God the Father, not the Second person of the Trinity praying to the First person of the Trinity. Now, of course it is admitted that the voicing of the prayer in human words and language is necessarily human, but is the prayer also "human"?
The problem it seems to me comes down to Christology. The Christian position has always been Christ is one person with two natures and two wills. The "two wills" is meant to safeguard the fact that Christ has two natures, in the sense that a nature comes with a will, and thus Christ having two wills safeguards the fact that Christ is both fully human and fully divine, not a mixture of the two in any sense. But orthodox Christology has similarly deny that a nature is its own actor, as if Christ has two separate wills in him warring over what to do. Christ is one actor, thus one person. Unlike humans who have one nature and thus our persons, natures and wills coincide, Christ's two natures are in one person and thus one act of willing (through two wills of course). The view that Christ's natures can subsist independent of His one person can be considered to be some variant of Nestorianism, which holds that Christ is two persons, two natures and two wills.
Thus, in embracing Chalcedon, it seems that we must reason in light of this orthodox doctrine of Christ's one person. Christ's natures are not personalized in any way, but rather it is Christ who acts according to either of his natures in whatever He does. In other words, Christ in His person is the actor, not His natures. Natures don't act, but persons do. Therefore, while it can be said in a human action that Christ acts to, for example, eat His lunch, according to His human nature, yet it is the one person of Christ who chooses to eat His lunch. Yes, such human actions are done according to His human nature. BUT, it is Christ's person who does so, according to His human nature.
What this implies for Holmes' interpretation of Christ's prayer is that we have a real problem here. According to Holmes' interpretation, which claims patristic support, Jesus' prayers on earth was done according to His human nature. So far, so good. But since Christ's natures don't act, it is Christ's one person that chooses to act according to His human nature. Or to emphasize, it is Christ's ONE PERSON who acts. In other words, yes, we hear the "authentically human voice of the incarnate Son pleading with God." But it is also the authentic voice of the one person of the SON who is pleading with God the Father. So, since it is the one and same person of the Son whether He is incarnated or not, does it really change the fact so that such interactions are not somehow intra-triune dialogues? The person of the Son remains the same pre-incarnated or incarnated. So why does the incarnation somehow makes the dialogue between the Father and the Son no longer an intra-triune dialogue?
Seeing as how Holmes claim patristic support, it is possible that such a conundrum was addressed by any of the Church Fathers. However, based so far on what I have read, I do not see how this rejection of the presence of intra-triune dialogues in time can be maintained. Not to mention that this idea of reading the Gospel accounts does not seem to me a natural way of reading Christ's interaction with His Father, which does suggest a genuine interpersonal relational interaction between God the Father and God the Son, rather than the triune God with the human nature of Christ.