Here's my go at the Tudor Family tree in the world where Arthur and Catherine have 12 children. I'd love any feedback ya'll have, especially for the Italian marriages, I'm not as familiar with Italy in this period.
Arthur I Tudor, King of England, b. 1586 m. Catalina Trastamara, Infanta of Aragon, b. 1485
1) Elizabeth Tudor, Princess of England, 1503, b. Charles V Habsburg, Holy Roman Emperor, b. 1500
2) Alfred, Prince of Wales, 1504 m. Isabella Aviz, Infanta of Portugal, b. 1503
3) Mary Tudor, Princess of England, b. 1506, m. João III Aviz, King of Portugal, b. 1502
4) Henry Tudor, Duke of Somerset, b. 1508 m. Anne Stewart, b. 1510 [1]
5) Katherine Tudor, Princess of England, b. 1509, m. James V Stewart, King of Scotland, b. 1512
6) Margaret Tudor, Princess of England, b. 1509, b. John Frederick I von Wettin, Elector of Saxony, b. 1503
7) Cecily Tudor, Princess of England, b. 1510, became a nun
8) Edmund Tudor, Duke of Hereford, b. 1512 m. Katherine Willoughby, Baroness Willoughby de Eresby, b. 1519
9) Arthur, Duke of Richmond, b. 1513 m. Anne Bourchier, Baroness Bourchier, b. 1517
10) Joan Tudor, Princess of England, b. 1515, b. Francis III Valois, Dauphin of France, b. 1518
11) John, Duke of Cambridge, b. 1517 m. Margaret Douglas, b. 1515
12) Edward Tudor, Duke of Bedford, b. 1518, m. Maud Percy, b. 1525 [2]
[1] Daughter of John Stewart, Duke of Albany and Anne de La Tour d’Auvergne. Catherine de Medici is never born so Anne inherits Auvergne and some of her fathers lands as well.
[2] Henry Percy and Mary Talbot manage one daughter before the relationship completely deteriorates, heiress to the Northumberland estates
Margaret Tudor, Lady of England, b. 1489 m. a) James IV Stewart, King of Scotland, b. 1473; b) Archibald Douglas, Earl of Angus, b. 1489; c) Henry Stewart, Lord Methven, b. 1495
a1) James Stewart, Duke of Rothesay, b. 1507, b. 1508
a2) Arthur Stewart, Duke of Rothesay, b. 1509, d. 1510
a3) James V Stewart, King of Scotland, b. 1513 m. Katherine Tudor, Princess of England, b. 1509
a4) Alexander Stewart, Duke of Ross, b. 1514, d. 1515
b5) Margaret Douglas, b. 1515, m. John, Duke of Cambridge, b. 1517
Henry Tudor, Duke of York, b. 1491 m. a) Marguerite of Angouleme, b. 1492, d. 1508; b) Elizabeth de la Pole, b. 1498
1a) Henry Tudor, Duke of York, b. 1506, m. Elizabeth Grey, Viscountess Lisle, b. 1505
2a) Arthur Tudor, Earl of Leicester b. 1507, m. Anne Boleyn, b. 1507
3b) Charles Tudor, Earl of Suffolk, b. 1517 m. Elizabeth Brooke, b. 1526
4b) Louise Tudor, b. 1519, m. Thomas Grey, Marquess of Dorset, b. 1517
5b) Isabel Tudor, b. 1521, m. Henry Clifford, Earl of Cumberland, b. 1517
6b) John Tudor, b. 1525, m. Catherine Howard, b. 1524
Mary Tudor, Lady of England, b. 1496, m. Louis XII Valois, King of France, b. 1496, d. 1515, no issue; Maximillian Sforza, Duke of Milan, b. 1493
1) Eleonora Sforza, b. 1518 m. Ercole II d’Este, Duke of Ferrara, b. 1508
2) Francesco Sforza, Duke of Milan, b. 1520 m. Caterina de Savoy, b. 1529
3) Enrico Sforza, b. 1528, m. Anna Gonzaga, b. 1531