If these passages from 1 Corinth 11:3 & 15:28 don't teach the eternal submission of Jesus to the Father, then how should I understand them?
On Sunday 25 Feb 2018, Dr Peter Masters preached on "The Light of Christ" from John 1. In it at about 39 minutes in online video he said some people believed in the eternal submission of the Son to the Father, but actually the Son's submission to the Father was only while he was on earth: there was/is no eternal submission. It is just an aside in his message, no evidence is given.
I confess I find this viewpoint baffling. (I had no idea that my answer here was remotely controversial: Is 1 Corinthians 15:27 problematic for trinitarians? )
With the greatest respect to all who hold this view, where is the biblical evidence for the absolute equality of Father and Son in their personal relations in eternity? Equality in divine nature does not require equality in relationship.
This is not just a quibble about words, but maybe it is close: after all, the Son wills and has aways willed in His Divine nature precisely what the Father wills: the Son's will has never been constrained to agree with the will of the Father: their Divine wills are and have always been in perfect harmony about everything.
Nevertheless, the Son is the Son and the Father is the Father: God calls us to obey our parents: Surely, this commandment is eternally obeyed by the Son of God.. He would not break one of His own commandments.
It is a wonder of my faith to believe that God Himself, in the Person of the Son of God, obeys: He is not hypocritical in calling us to honour our parents and those in authority, by obedience to them.. and if even God (the Son) obeys then how much more should we?
"If yes, [i.e. if the submission is eternal] how so if the submission is yielding to the will of another and the will is a property of nature/being?"
The ability to yield is the property of a nature, but yielding to the will of another person is the act of a person. The three persons of the Godhead have the same nature but are not identical in their actions: the Son went to the cross, not the Father, nor the Holy Spirit; "This is my beloved Son, listen to him" was said by the Father not the Son. The Son yielding to the will of the Father is not inconsistent with the Son having the same nature as the Father.
Now, after His resurrection, the Son of God is both God and man for all future eternity. In such a condition He, of course, offers up all to God (1 Cor 15:28).. the resurrected Lord, as a resurrected creature, offers all up to God. 1 Cor 11:3 is also speaking of the person of Christ as the God-Man. The head of the man, our Lord Jesus Christ, is God.
("If no, how do I then think through these texts which seem to communicate an eternal submission of the Son well after the incarnation?"
In this view the submission is not only "after the incarnation" but also before.)