Family of Sigismund the Old:
Sigismund I (1467-1548) Grand Duke of Lithuania 1506-1548, King of Poland 1507-1548 m. a) 1512 Barbara Zapolya (ca 1495-1521) b) 1523 Eleanor of Austria (1498-1558)
1a) Hedwig (1513-1573) m. 1530 Francis I King of France
2a) Anna (1515-1562) m. 1532 Joachim II Elector of Brandenburg
3a) Sigismund II (1517-1588) Grand Duke of Lithuania, King of Poland 1548-1588 m. Dorothea or Christina of Denmark (?) His stepmother would be propably in favour of such marriage and would like to see her niece as Queen of Poland.
4a) Elizabeth (1519-1591) m. Albert of Brandenburg-Kulmbach (who would not lose father in 1527-Casimir Hohenzollern does not need for Ferdinand's case in Hungary, and heavy intermarriage between Jagiellons and Hohenzollerns is justified-if Louis III of Hungary wants Imperial throne, it would be good for Jagiellons to have Hohenzollern support).
5a) Sophia (1521-1576) m. either her cousin Louis III of Hungary or some duke of HRE, perhaps Duke of Lorraine? She is sister of French Queen and heir of Spanish and Burgundian lands, so why not? Or Severinus of Saxony-where he would be raised after Ferdinand Habsburg dies?)
6b) Albert I (1525-1579) King of Naples 1554-1579, King of Spain 1556-1579 m. a) 1545 Maria Manuela of Portugal (1527-1551) b) 1554 Mary Tudor, Queen of England (1516-1568, let's have her living a little longer) c) possibly Hungarian cousin
1a) Charles II (born 1547) King of Spain
2a) Eleanor (born 1550) m. Duarte II of Portugal (?)*
3a) Mary (born and died 1551)
4b) Henry IX (born 1555) King of England, Duke of Burgundy
Now son of Louis II of Hungary and Mary of Austria:
Louis III (1524-1592) King of Bohemia and Hungary 1526-1592, Archduke of Austria, Holy Roman Emperor 1556-1592 m. either Polish cousin or Hohenzollern cousin Kunigunde of Brandenburg-Kulmbach (for Hohenzollern support in Imperial election)
*Now Portugal: Charles II Jagiellon would have the best genealogical claim to the throne, but @Kellan Sullivan mentioned, that Maria Manuela renounced her rights upon marriage, thus after John III dies, he should be succeeded by his nephew Duarte of Guimarães.