Question: Who was married to Sigismund III Vasa, and mother to Władysław IV Vasa?

Context paragraphs:
Władysław IV Vasa: Władysław IV Vasa (Polish: "Władysław IV Waza" ; Russian: Владислав IV Ваза , "Vladislav IV Vaza" ; Latin: "Vladislaus IV Vasa" or "Ladislaus IV Vasa"; Lithuanian: "Vladislovas Vaza" ; 9 June 1595 – 20 May 1648) was a Polish prince from the Royal House of Vasa.  He reigned as King of Poland and Grand Duke of Lithuania from 8 November 1632 to his death in 1648.

Shuysky Tribute: Shuysky tribute was the act of homage of the deposed Tsar Vasily IV of Russia and his retinue to the Polish King Sigismund III Vasa and teenage prince Władysław (the then candidate to the Russian throne) on October 29 1611 in the Senate Hall of the Royal Castle in Warsaw.

Constance of Austria: Constance of Austria (German: "Konstanza" ; Polish: "Konstancja" ; 24 December 1588 – 10 July 1631) was queen of Poland as the second wife of King Sigismund III Vasa and the mother of King John II Casimir.

War of the Polish Succession (1587–88): The War of the Polish Succession or the Habsburg-Polish War took place from 1587 to 1588 over the election of monarch after the death of King of Poland and Grand Duke of Lithuania Stephen Báthory.  The war was fought between factions of Sigismund III Vasa and Maximilian III, with Sigismund eventually being crowned King of Poland and Grand Duke of Lithuania.  Two major battles of this conflict included the Siege of Kraków, in which Maximilian III failed to capture the capital of the Commonwealth, and the Battle of Byczyna, in which Maximilian was forced to surrender.  Sigismund's victory was significantly the doing of Chancellor and Hetman Jan Zamoyski, who stood behind both the political intrigue and the military victories of this conflict.

Anna Jagiellon: Anna Jagiellon (Polish: "Anna Jagiellonka" , Lithuanian: "Ona Jogailaitė" ; 18 October 1523 – 12 November 1596) was Queen of Poland and Grand Duchess of Lithuania in her own right from 1575 to 1586.  She was a daughter of Polish King Sigismund I the Old and his Italian wife Bona Sforza.  Despite multiple proposals, she remained unmarried until the age of 52.  After the death of King Sigismund II Augustus, her brother and the last male member of the Jagiellon dynasty, Anna's hand was sought by pretenders to the Polish–Lithuanian throne to maintain the dynastic tradition.  She was elected, along with her then-fiancé Stephen Báthory, as co-ruler in the 1576 royal election of the Polish–Lithuanian Commonwealth.  Their marriage was a formal arrangement and distant.  Báthory was preoccupied with the Livonian War, while Anna spent her time in Warsaw on local administrative matters and several construction works.  After Báthory's death in December 1586, she had an opportunity to claim the throne for herself (she was co-ruler and not merely a consort), but did not even attempt it.  Instead, she promoted her nephew Sigismund III Vasa, establishing House of Vasa on the Polish–Lithuanian throne for the next eighty years (1587–1668).

John II Casimir Vasa: John II Casimir (Polish: "Jan II Kazimierz Waza" ; German: "Johann II.  Kasimir Wasa" ; Lithuanian: "Jonas Kazimieras Vaza" ; 22 March 1609 – 16 December 1672) was King of Poland and Grand Duke of Lithuania during the era of the Polish–Lithuanian Commonwealth, Duke of Opole in Upper Silesia, and titular King of Sweden 1648–1660.  In Poland, he is known and commonly referred as Jan Kazimierz.  His parents were Sigismund III Vasa (1566–1632) and Constance of Austria (1588–1631).  His older brother, and predecessor on the throne, was Władysław IV Vasa.

Åbo Bloodbath: The Åbo Bloodbath of 10 November 1599 was a public execution in the Finnish town of Turku (Åbo), then part of the Kingdom of Sweden, in the context of the War against Sigismund and the Club War.  Sweden was by then in the final phase of a civil war, with one faction supporting king Sigismund III Vasa, who also was king and Grand Duke of Poland-Lithuania, and another faction supporting duke Charles of Södermanland, the later Charles IX, Sigismund's paternal uncle.  After winning the upper hand in the dispute, Charles crushed the last resistance to his rule, particularly in Finland, while Sigismund had already retreated to Poland.

Adam Jarzębski: Adam Jarzębski (c. 1590 in Warka – c. 1648 in Warsaw) was an early Baroque Polish composer, violinist, poet, and writer.  The first documented mention of Jarzębski was in 1612, when he became a member of the chapel of John Sigismund, Elector of Brandenburg in Berlin.  After he had stayed in Italy for a year (1615–16), he became a member of the royal musical establishment, first at the court of Sigismund III Vasa and then of Władysław IV.  He was held in great esteem by the royal court and was very popular among the members of the patriciate of Warsaw.  In 1635 he managed the construction of the royal palace at Ujazdów.  In 1643 he published a literary work "Gościniec, albo krótkie opisanie Warszawy" ("The Main Road, or a Short Description of Warsaw") describing the customs and the musical life of the town.  He died in Warsaw in 1649.  He was an outstanding figure in the history of the Polish culture of the 17th century.

Battle of Gniew: The Battle of Gniew or the Battle of Mewe was fought during the Polish–Swedish War (1626–1629), between Sweden and the Polish–Lithuanian Commonwealth from 22 September with initial skirmishes, to the main battle of 1 October 1626.  Both the Swedish and Polish army were commanded by their kings – Gustavus Adolphus of Sweden and Sigismund III Vasa.  The battle ended with a victory for Sweden.  However, Polish and Swedish armies had different objectives.  Sigismund Vasa wanted to protect Gdańsk from besieging.  Gustav had to protect Gniew, which was important for the prestige for his army.

Sigismund III Vasa: Sigismund III Vasa (also known as "Sigismund III of Poland", Polish: "Zygmunt III Waza" , Swedish: "Sigismund" , Lithuanian: "Žygimantas Vaza" , English exonym: "Sigmund"; 20 June 1566 – 30 April 1632

Supporting paragraphs: John II Casimir Vasa Constance of Austria
Answer: Constance of Austria