What you might actually see happen is after the death of Prince Arthur, of Wales, is a York rebellion in 1502.
Henry VII flees to Aragon, aboard the ship carrying the widowed, Catherine of Aragon.
Queen Elizabeth of York, is crowned as Ruling queen, by the York led government. Margaret Tudor, at 13, becomes heir presumed and is married to Henry Pole was the oldest son of Margaret Pole, 8th Countess of Salisbury (herself being the only surviving daughter of George Plantagenet, 1st Duke of Clarence, who was the younger brother of King Edward IV and King Richard III.)
Queen Elizabeth is married off again to her cousin, Edmund de la Pole, 3rd Duke of Suffolk, the last surviving heir-apparent to his maternal uncle, Richard III. He is created as Prince Edmund, Grand Duke of Suffolk, however two years into the marriage, Elizabeth dies on the, 11th July, 1505, while giving birth to a stillborn baby girl.
Margaret, who took the her mothers and husband's royal house name, four months shy of 16, is crowned Queen Margaret I of England, with Henry becoming, the first Duke of York, since the death of Richard of Shrewsbury.
List of Monarchs
Monarchs of England
1457 - 1502: Henry VII (House of Tudor)
1502 - 1505: Elizabeth I (House of York)
1505 - 1541: Margaret I (House of York)
1541 - 1542: Arthur I (House of York)
1542 - 1587: Mary I (House of York)
Monarchs of England, France, and Ireland
1587 - 1625: Francis I/III (House of Valois-Orléans-Angoulême)
1625 - 1669: Henry/ Henri VIII/III (House of V.-O.-A.)
1669 - 1680: First Civil War
1680 - 1692: Henry/ Henri IX/IV (House of Windsor-Louvre)
1692 - 1706: Henry/ Henri X/V (House of Windsor-Louvre)
Monarchs of England, France, Scotland and Ireland
1706 - 1747: William III/I (House of Windsor-Louvre)
1747 - 1766: Edward VI/I (House of Windsor-Louvre)
1766 - 1779: William IV/II (House of Windsor-Louvre)
1779 - 1801: Francis II/IV (House of Windsor-Louvre)
1801 - 1809: Second Civil War
1809 - 1827: Francis II/IV (House of Windsor-Louvre)
1827 - 1852: John II/III (House of Saxe-Coburg-Saalfeld)
1852 - 1876: William V/III (House of Saxe-Coburg-Saalfeld)
1876 - 1912: Edward VII/II (House of Saxe-Coburg-Saalfeld)
1912 - 1913: Henry/Henri XI/VI (House of Saxe-Coburg-Saalfeld)
1913 - 1919: Great World War
1919 - 1932: Charles I/XI (House of Kent-Normandy)
1932 - 1957: Charles II/XII (House of Kent-Normandy)
1957 - 1992: Charles I/XI (House of Kent-Normandy)
1992 - Present: John III/IV (House of Kent-Normandy)