Arthur was given his own household at Ludlow, just as Elizabeth's brother had before him, demonstrating that traditions would continue under the new regime. A royal princess was found for him to marry, and fate would ensure that Katherine of Aragon became queen of England.
As Arthur was being trained for greatness, two brothers were added to the family. Henry and Edmund were certainly welcomed by parents and countrymen alike, though their birth was not as celebrated as Arthur's. Like all good medieval parents, Elizabeth and Henry planned to dedicate one son to the church. Though it is difficult for those of us who know his story to imagine it, Henry probably believed for much of his young life that he would someday become the Archbishop of Canterbury.
The difficulty of bearing sons would go on to be a defining element of the Tudor dynasty. Henry VII left his throne to his son in 1509. Henry VIII was a fit, intelligent, and virile 18 year old when his father died, and the future seemed bright. He married his brother's widow and could have never foreseen his challenge to bear an heir.
Where a multitude of sons may have had unforeseeable consequences to the Plantagenet dynasty, eventually causing it to be snuffed out entirely by the Wars of the Roses, a painful lack of sons become the death toll of the Tudor dynasty.