Ok I think I have a solid scenario for this POD:
1484: Edward of Middleham, the Prince of Wales, suffers an illness but pulls through, managing to survive and thus emerges healthy, but weaker than prior to the illness. He, however, begins to regain his strength and by August is proclaimed stronger than ever.
1485: Richard III of England begins negotiations with Spain to marry Edward to either the Catholic Monarchs' eldest daughter or their second, Isabella or Joanna of Aragon. Richard hopes for Isabella, but the Catholic monarchs initially favour a match between the Prince of Wales and Joanna. During this time, the Queen of England, Anne Neville, dies, leaving the King of England a widower with one child, Managing to use this to his advantage, he contracts a marriage to the Infanta Joanna of Portugal, to be completed when and if the menace of Henry Tudor, pretender to the Throne, is dealt with. Agreeing, he leaves London with his son as Regent, a purely symbolic act but one that shows he has faith in the future. The battle between the Yorkist and Tudor armies is bloody, but ultimately Richard wins out. Taking Henry Tudor into his custody, he does not have him executed, but instead offers to allow him the privileges of his father as Earl of Richmond, and to find him a suitable bride. Tudor agrees, becoming a footnote in history.
1486: The Infanta Joanna arrives in England, miserable. However, she is greeted by such fanfare that even she is impressed, although that won't end her bitter correspondence with her family in Portugal. Her cousin, the Duke of Beja and Viseu, would later in the year marry the King of England's niece Elizabeth of York, as the marriage pact had agreed to. Late in the year, Queen Joanna would announce her first pregnancy, while the marriage treaty between England and Spain was completed by a betrothal between Edward of Middleham and Isabella of Aragon.
1487: The birth of the Prince John of England, Duke of York, was a major boost for Richard III of England. With only a son who had proved unhealthy in the past and was still somewhat weaker than hoped, and having just come off the death of his first wife and a major rebellion, it was hope for the future. This was compacted by a wedding later in the year as the Infanta Isabella of Aragon arrived in England, flanked by 25 beautiful Spanish ladies-in-waiting. Finding herself thrilled with her new husband, the Infanta was pleasing to her new family. In Portugal, within weeks of the announcement of a son to the Infanta Joanna, the Duke of Beja and Viseu mysteriously died, leaving his bride pregnant with their first child. This child, a daughter, was named Beatrice of Viseu.
1488: The birth of another child with the Infanta Joanna, another Prince, named Richard, came as yet another great boon for the King of England. With his three sons, Richard felt secure enough to set sail to Calais, where he began his attack in France. Partially a continuation of the Hundred Years War, partially an attempt to get the France back for backing Henry Tudor, the King of England took a few cities and townships, not quite reaching Paris, before the diplomacy began.
1489: Having treated 6 months, the King of England would emerge victorious in his battle for France, although not overly victorious. Richard would be granted an extension of the land around Calais, along with various townships around that area, and a annuity. Thus, English interests in France were heightened, but not to the extent that many had hoped. Unsatisfied with his war, the King of England returned to London with much fanfare. Traveling with his army, he shortly after travel to Ireland to begin sorting out the issue of a pretender to his throne, a young man who claimed to be his nephew Richard. Ensuring the boy was captured, the King of England would have him and his conspirators executed.
1490: The birth of a Princess to the King of England and his wife, the Queen Joanna, was to come early in the year. The Princess Cecily would act as a conciliatory for Richard to use in France, as he offered the Princess to the first son of the King of France. Charles VIII of France, yet unmarried, would accept this potential betrothal. It was this year that the King of Scotland was contracted to marry the Infanta Catalina of Aragon, youngest daughter of the Catholic Monarchs.
1491: The death of the Queen of England early in the year caused much sorrow in London. Having lost a second wife in less that a decade, Richard III of England would fall into a deep grief, becoming intensely focused on the subject or ruling. The birth of a grandson in the form of Edward of Wales managed to brighten the mood, but this joy was undercut by the infant's ill health.
1492: The death of two of the royal family's children caused much sorrow in the court, not quite recovered from the death of Joanna of Portugal. First, Cecily of England died, and within a week her nephew, Edward of Wales also died.
Richard III of England (b.1452: d.1498) m. Anne Neville (b.1456: d.1485) (a), Joanna of Portugal (b.1452: d.1491) (b)
1a) Edward of Middleham, Prince of Wales (b.1473: d.1497) m. Isabella of Aragon (b.1470: d.1519) (a)
1a) Edward of Wales (b.1491: d.1492)
2a) Richard IV of England (b.1492)
3a) Miscarriage (c.1494)
4a) Anne of England (b.1496)
2b) John III of Portugal (b.1487: d.1515) m. Beatrice of Viseu (b.1487: d.1552) (a)
1a) Edward II of Portugal (b.1509)
2a) Isabella of Portugal (b.1513)
3b) Richard of England, Duke of Gloucester (b.1488)
4b) Cecily of England (b.1490: d.1492)