Question: Anna Jagiellon, 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, which member of the powerful House of Sforza, which ruled the Duchy of Milan since 1447?

Context articles: Barbara Zápolya
Barbara Radziwiłł
Goštautai
Catherine of Austria, Queen of Poland
Bona Sforza
Anna Jagiellon
Isabella Jagiellon
Stephen Báthory
Aleksander Chodkiewicz
Helena of Moscow

Barbara Zápolya (1495–1515) was Queen of Poland and Grand Duchess of Lithuania as the first wife of King Sigismund I the Old.
 Marriage to Barbara represented an alliance between Sigismund and the House of Zápolya against the Habsburgs in succession disputes over the throne to the Kingdom of Hungary.
 The alliance was short-lived as the renewed Muscovite–Lithuanian War forced Sigismund to look for Habsburg allies.
 The marriage was loving, but short.
 Barbara was the mother of Hedwig, Electress of Bradenburg, but died soon after the birth of her second daughter Anna.
Barbara Radziwiłł (Polish: "Barbara Radziwiłłówna" , Lithuanian: "Barbora Radvilaitė" ; 6 December 1520/23 – 8 May 1551) was Queen of Poland and Grand Duchess of Lithuania as consort of Sigismund II Augustus, the last male monarch of the Jagiellon dynasty.
 Barbara, a great beauty and already widowed, became a royal mistress most likely in 1543 and they married in secret in July or August 1547.
 The marriage caused a scandal; it was vehemently opposed by Polish nobles, including Queen mother Bona Sforza.
 Sigismund Augustus, assisted by Barbara's cousin Mikołaj "the Black" Radziwiłł and brother Mikołaj "the Red" Radziwiłł, worked tirelessly to gain recognition of their marriage and to crown Barbara as Queen of Poland.
 They succeeded and Barbara's coronation was held on 7 December 1550 at Wawel Cathedral.
 However, her health was already failing and she died just five months later.
 Even though it was brief, her reign propelled the Radziwiłł family to new heights of political power and influence.
Goštautai (Lithuanian plural form), masculine Goštautas and feminine form Goštautaitė ("Polish" original, after Kasper Niesiecki - Gastoldowie, later transformed into Gasztołdowie) were a Lithuanian noble family, one of the most influential magnate families during the 15th and early 16th centuries.
 Their only serious rivals were the Kęsgailos, and from the end of the 15th century the fast rising in power and influence Radziwiłł family clan.
 It appears from the Latin original spelling of their name Gastoldus which is a variation of "castaldius" that they had been close to the Grand Dukes and that their function was to oversee ducal demesne.
 Most power family gained during the reign of Casimir Jagiellon.
 The castaldius of Vytautas, Andrius Goštautas might have been a voivode of Vilnius and Kreva, and father of Jonas, appears to have been the precursor of the family growth.
 The majority of the family's possessions (lands) were in the western part of the Duchy and eastern ethnic Lithuania.
 After the death of the last scion of the family, Stanislovas Goštautas, the Polish King and Grand Duke of Lithuania Sigismund II Augustus inherited his possessions as a matter of right, per Grand Duchy of Lithuania law.
Catherine of Austria (Polish: "Katarzyna Habsburżanka" ; Lithuanian: "Kotryna Habsburgaitė" ; 15 September 1533 – 28 February 1572) was one of the fifteen children of Ferdinand I, Holy Roman Emperor and Anna of Bohemia and Hungary.
 In 1553, she married Polish King Sigismund II Augustus and became Queen consort of Poland and Grand Duchess consort of Lithuania.
 Their marriage was not happy and they had no issue.
 After a likely miscarriage in 1554 and a bout of illness in 1558, Sigismund became increasingly distant.
 He tried but failed to obtain a divorce from the pope.
 In 1565, Catherine returned to Austria and lived in Linz until her death.
 Sigismund died just a few months after her bringing the Jagiellon dynasty to its end.
Bona Sforza (2 February 1494 – 19 November 1557) was a member of the powerful House of Sforza, which ruled the Duchy of Milan since 1447.
 In 1518, she became the second wife of Sigismund I the Old, the King of Poland and Grand Duke of Lithuania.
 Their marriage lasted 30 years until Sigismund's death in 1548.
 Ambitious and energetic, Bona became heavily involved in the political life of Poland–Lithuania.
 To increase state revenue, she implemented various economic and agricultural reforms, including the far-reaching Wallach Reform in the Grand Duchy of Lithuania.
 Her reforms made her the richest landowner in the Grand Duchy.
 In foreign policy, she opposed the Habsburgs and sought to secure her eldest daughter Isabella Jagiellon in the Kingdom of Hungary.
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).
Isabella Jagiellon (Hungarian: "Izabella királyné" ; Polish: "Izabela Jagiellonka" ; 18 January 1519 – 15 September 1559) was the oldest child of Polish King Sigismund I the Old and his Italian wife Bona Sforza.
 In 1539, she married John Zápolya, Voivode of Transylvania and King of Hungary, becoming Queen consort of Hungary.
 At the time Hungary was contested between Archduke Ferdinand of Austria who wanted to add it to the Habsburg domains (see Royal Hungary), local nobles who wanted to keep Hungary independent (see Eastern Hungarian Kingdom), and Sultan Suleiman the Magnificent who saw it as a vassal state of the Ottoman Empire (see also Little War in Hungary).
 While Isabella's marriage lasted only a year and a half, it did produce a male heir – John Sigismund Zápolya born just two weeks before his father's death in July 1540.
 She spent the rest of her life embroiled in succession disputes on behalf of her son.
 Her husband's death sparked renewed hostilities but Sultan Suleiman established her as a regent of the eastern regions of the medieval Kingdom of Hungary on behalf of her infant son.
 The region developed as a semi-independent buffer state noted for its freedom of religion.
 Ferdinand, however, never renounced his claims to reunite Hungary and conspired with Bishop George Martinuzzi who forced Isabella to abdicate in 1551.
 She returned to her native Poland to live with her family.
 Sultan Suleiman retaliated and threatened to invade Hungary in 1555–56 forcing nobles to invite Isabella back to Transylvania.
 She returned in October 1556 and ruled as her son's regent until her death in September 1559.
Stephen Báthory (Hungarian: "Báthory István" ; Polish: "Stefan Batory" ; Belarusian: Стэфан Баторы ; Lithuanian: "Steponas Batoras" ; Romanian: "Ștefan Báthory" ; 27 September 1533 – 12 December 1586) was Voivode of Transylvania (1571–76), Prince of Transylvania (1576–86), from 1576 Queen Anna Jagiellon's husband and "jure uxoris" King of Poland and Grand Duke of Lithuania (1576-1586).
Aleksander Chodkiewicz (Lithuanian: "Aleksandras Chodkevičius" , Belarusian: Аляксандар Хадкевіч ; ca. 1475 – 28 May 1549) was a noble from the Grand Duchy of Lithuania, founder of the Supraśl Orthodox Monastery.
 He inherited vast possessions from his father Ivan Chodkiewicz, which made him 11th wealthiest person in the Grand Duchy according to the military census of 1528.
 Via his mother Jawnuta (Agnieszka) of the Belsky family, he was second cousin to Kings of Poland John I Albert, Alexander Jagiellon, and Sigismund I the Old.
 Chodkiewicz quickly gained influence under Alexander Jagiellon, becoming royal marshal.
 However, after Alexander's's death in 1506 his career stagnated.
 He supported Queen Bona Sforza, gaining her favor and becoming starost of Brest in 1528.
 The peak of his career came in 1544 when young Sigismund II Augustus, still influenced by his mother, appointed Chodkiewicz as voivode of Nowogródek and his son Hieronim as castellan of Trakai.
Helena Ivanovna of Moscow (Russian: Елена Ивановна ; Lithuanian: "Elena" ; Polish: "Helena Moskiewska" ; 19 May 1476 – 20 January 1513) was daughter of Ivan III the Great, Grand Prince of Moscow, and an uncrowned Grand Duchess of Lithuania and Queen of Poland as she would not convert from Eastern Orthodoxy to Catholicism.
 Her childless marriage to Grand Duke of Lithuania and later King of Poland Alexander Jagiellon was a constant source of tension between the Grand Duchy of Moscow and the Grand Duchy of Lithuania.
 Instead of guaranteeing peace, Helena's marriage gave her father Ivan III an excuse to interfere in Lithuanian affairs accusing Alexander of mistreating Helena and repressing Orthodox believers.
 This became the pretext to renew the Muscovite–Lithuanian War in 1500.
 The war ended with a six-year truce in 1503; the Grand Duchy of Lithuania lost about a third of its territory.
 Despite political tensions and religious differences, the marriage was a loving one and the royal couple was close.
 After her husband's death in 1506, Helena wanted to return to Moscow but was not allowed.
 When she planned to run away, she was arrested and reportedly poisoned.