This is from John Welch’s May 2011 Maeser Distinguished Faculty Lecture. I love the insight into Matthew 21:27-29.
After Jesus’ triumphal entry into Jerusalem, the Chief Priests approached him, in the Temple, and demanded: “By what authority doest thou these things? and who gave thee this authority?” Jesus answered by telling a story about a certain man who had two sons. When asked to go down and work in the vineyard, the first son, initially refused, but then he went, while the other initially said yes but then does not go, or so it seems. This parable may be useful in parenting, and it can be read at that level; but remember, that’s not what Jesus was asked about. With the question of authority in mind, as I read this parable in the Greek, something jumped off the page at me. Think about it: When did a certain father have two sons, one who went and the other who did not? When did the first (the firstborn) say, “ou thelo,” which in Greek means “I will it not,” or “I’d rather not” or “it is not my will.” As the Greek continues, that son reconciled himself (not repented himself) and went. In contrast, the “other” (the heteros) son simply said, “Ego,” meaning “I.” But “I what”? Readers must fill in this blank. In this verse, the word “go” in the King James Version is italicized because it has only been implied there. One might as well supply other words: “I . . . will have it my way,” or “I . . . will get the glory.” In any event, this egotistic son did not go. As Latter-day Saints, we can easily but unexpectedly see at this deeper level how this unassuming little parable answers the all-important questions about Jesus’ authority. He received it from the Father in the council in heaven when he was commissioned to go down and do, not his will, but the will of the Father.
I looked at the word translated "repent" (μεταμεληθεὶς) in verse 28. In Vincent's Word Studies posted at http://bible.cc/matthew/21-29.htm we find "This is a different word from that in Matthew 3:2; Matthew 4:17; μετανοεῖτε, Repent ye. Though it is fairly claimed that the word here implies all that is implied in the other word, the New Testament writers evidently recognize a distinction, since the noun which corresponds to the verb in this passage (μεταμέλεια) is not used at all in the New Testament, and the verb itself only five times; and, in every case except the two in this passage (see Matthew 21:32), with a meaning quite foreign to repentance in the ordinary gospel sense. Thus it is used of Judas, when he brought back the thirty pieces (Matthew 27:3); of Paul's not regretting his letter to the Corinthians (2 Corinthians 7:8); and of God (Hebrews 7:21). On the other hand, μετανοέω, repent, used by John and Jesus in their summons to repentance (Matthew 3:2; Matthew 4:17), occurs thirty-four times, and the noun μετάνοια, repentance (Matthew 3:8, Matthew 3:11), twenty-four times, and in every case with reference to that change of heart and life wrought by the Spirit of God, to which remission of sins and salvation are promised. It is not impossible, therefore, that the word in this passage may have been intended to carry a different shade of meaning, now lost to us. Μεταμέλομαι, as its etymology indicates (μετά, after, and μέλω, to be an object of care), implies an after-care,..."
The words translated "will not" could also be translated would not, do not desire to, or do not find pleasure in.
So it is my (RLG) understanding that verse 28 could be rendered that the first son said "it is not my will, but then he cared and went."
So these verses can be interpreted at least two ways. The common way is comparing those who initially reject God's word but later come to care for God and change their lives with the hypocrites who represent they are doing will of the father but do not. John Welch points out the the other: the examples of Jesus and Lucifer. The later interpretation related to us is that as parents or as church members, our authority to act comes from accepting calls to do the Father's will. The Lord commissions us or places his name upon us and sends us forth to do his will. Because we care (love) we accept the call and go.