Jacob was promised the land of Canaan for a possession; yet his brother Esau came into his own kingdom long before, according to Genesis 36 and Deuteronomy 2, despite the word given to Rebekah, "Two nations are in thy womb, and two manner of people shall be separated from thy bowels; and the one people shall be stronger than the other people; and the elder shall serve the younger." (Genesis 25:23) If Jacob was the Lord's anointed, why did Esau prosper even as his Jacob's family was reduced to slavery?
There are many ways to approach this highly interesting question, which I will outline here. First, God told Abram that his descendants would not inherit the Promised Land until “they [the Egyptians, as we learn later] shall afflict them [the Israelites, as they will come to be called] four hundred years” (Gen 15:13). It is enough simply to say that Jacob and his sons could not come into their own land, as Esau did, without rendering this prophecy false.
But look also at the reason God gave to Abram for the delay: “the iniquity of the Amorites is not yet full.” This suggests that the Lord would not approve the extirpation of whole peoples by his own chosen people, and the transference of their land, except as just punishment. Moreover, perhaps the Israelites could not serve as the instruments of his holy wrath unless they themselves had been properly humbled.
Throughout the narrative of Genesis and indeed the whole Pentateuch, God’s chosen representatives are made to wait, even as their relatives and enemies prosper. As Abram waited for an heir, his brother Nahor and his nephew Lot reproduced without difficulty. Hagar produced a son as soon as she tried, after Sarai waited decades. Isaac and Rebekah had to wait 20 years, as Ishmael began his family. Esau had at least three wives (quite possibly four) before Jacob had even one. In short, the Lord taught through these examples that the emergence of the seed through which he would fulfill his promise was dependent entirely upon his own good pleasure, in his own time.
Then, while Jacob was blessed with a large family and wealth like his father and grandfather, his brother had not only that, but made his sons into Dukes (or Chiefs) in a land given to them by God “for a possession” (Deut 2:5); soon after that, even as the Israelites toiled in slavery, Esau’s children “had destroyed them [the Horites of Seir] from before them, and dwelt in their stead” (Deut 2:12). Later, as the newly freed Israelites venture through Sinai and wander in the wilderness, they encounter tribes descended from Abraham and Isaac that are established and prosperous. The result was humiliating for a people promised by God to inherit a land flowing with milk and honey, through whom all the nations would be blessed.
Only later, in the Psalms and wisdom literature, is it stated explicitly and repeatedly that the Lord requires patience and humility, and that the prosperity of the wicked must be endured. “Rest in the Lord, and wait patiently for him: fret not thyself because of him who prospereth in his way, because of the man who bringeth wicked devices to pass.” (Ps 37:7)
Rather than "humiliated," the children of Israel were instead "humbled," and, it seems, deliberately so. It is not unlikely that Jacob and his sons were themselves chastised for their various sins by their having finally to bow down to their brother, as according to his prophetic dreams, with their punishment even extending to the fourth generation by the captivity in Egypt. After that, they were humbled and shown to be wholly dependent upon the Lord, and upon their release, were a people better prepared to be “a kingdom of priests, and an holy nation.” (Ex 19:6) This was a thing far greater and more difficult than the mere capture of a pagan nation like Seir; because it required that humility and patient faith in the providence of the Lord be instilled into an entire nation, it was not a thing that God chose to do quickly, not with the rough clay of fallen humanity.