Well it didn't begin there; strife within the Vasa family was, in part, the cause of multiple uprisings in Sweden and decades of war between Sweden and Poland (1600-11, 1617-818, 1621-25, 1626-29, 1655–60 etc) both before and after the 30 Years War.

To give the necessarily much-abridged and simplified version: King Gustav Vasa (1492-1560) of Sweden had consolidated royal power and introduced the protestant reformation into Sweden. He had thee sons who were to become kings: Erik, Johan and Karl. The infighting started under Erik's rule (as Erik XIV), when his brother Johan, duke of Finland, married the catholic princess Catherine Jagiellon of Poland. This caused great distrust in Erik, who suspected of his brother of conspiring with the Polish-Lithuanian commonwealth to take power.

So he threw his brother in jail. First at Åbo castle, later Gripsholm. John was kept in fairly comfortable accommodations though, and in solidarity with her husband, Catherine joined him, and they would ultimately spend four years in prison there. It is there, in prison at Gripsholm, that the future king Sigismund is born in 1566. Meanwhile, Erik XIV was in correspondence with Ivan IV (the Terrible) of Russia and was plotting to extradite Catherine to Russia, where Ivan, a former suitor of Catherine's, seemed to have wanted her as a hostage for negotiations with Poland. Both Ivan and Erik had proposed marriage to Elizabeth I of England and failed; Erik then tried another strategy and proposed to Mary Stuart, but ultimately he married a commoner; Karin Månsdotter. This weakened Erik's position with the nobility further, already weak from having prosecuted aristocrats like Nils Sture, who he saw as potential threats.

1567 was Erik's 'year of misfortune'. His mental health was in a bad state; he was acting erratically; he'd personally murdered Nils Sture in his cell without obvious reason or provocation. He obsessed over delusional ideas, ordered a bunch of other prisoners killed, fled the capital and was retrieved hiding in disguise in the countryside. A lot of stuff. So the royal council decided to take over the actual ruling and ordered Johan released from prison in October 1567.

Johan wasted no time amassing support among the nobility to depose his brother. The king's behavior had made that support very easy to get. Within a year (September 1658), with Johan's forces gathered outside Stockholm, the city surrendered. In January he was crowned Johan III, and he immediately threw his brother in prison. He would be moved periodically from castle to castle for the next decades, due to Johan's fears of conspiracy, and he suffered more bouts of poor mental health before he died in 1577 from the arsenic his brother was having him fed with. (Meanwhile, Ivan IV would allegedly kill his own son in a fit of rage in 1581)

While Johan was ruling in Sweden, Sigismund (who was always closer to his mother) was elected as the Catholic king of Poland (Zygmunt III Waza) in 1587, while his father remained king in Sweden. (as an aside on religion; Johan made several overtures to try to reconcile the schism between the church of Sweden and Vatican, but without any success; Sweden became increasingly Lutheran) When Johan died at the end of 1592, there was a problem; Sigismund was next in line to be king of Sweden; but he couldn't be in two countries at once. The Polish Sejm was also wary of Sweden, and allowed him to go to the country for a limited time to be crowned (as Sigismund I of Sweden) and negotiate a solution. The deal reached was to allow Sigismund to remain the nominal king of Sweden but the day-to-day ruling would be handled by a viceroy, his uncle Karl.

Karl began to build his power-base, at the riksdag meeting of Söderköping 1595, he argued that he as viceroy be granted almost royal powers, but this was successfully defeated by the nobility. But Sigismund also disapproved of the decisions made in Söderköping and opposed them, which Karl used to call a new riksdag in Arboga in 1598. In the meantime he'd encouraged a peasant uprising in Finland against the Sigismund-loyal lord of Åbo castle, Clas Fleming. At the Arboga Riksdag, Karl appealed to the peasantry, playing on their dislike of the nobility and anti-catholicism, and managed to get himself confirmed as a viceroy with far-reaching powers. He began an open armed conflict against Sigismund, leading troops to capture royal castles in Sweden and Finland. Sigismund responded with troops from Poland and local loyalists, he had the support of much of the Swedish nobility and clergy who still considered him the rightful king, yet he was ultimately not victorious. This short war lasted with Karl's victory in 1599, but Karl would consolidate his power by executing his enemies (e.g. the Linköping Bloodbath of 1600) before having himself declared king. Karl was crowned as king Karl IX in 1604 and would rule until 1611, when his son Gustav II Adolf (or Gustavus Adolphus), cousin of Sigismund, took over.

Sigismund never gave up hope of reclaiming the Swedish throne though, and Sigismund's sons would retain their claim on the Swedish throne until John II Casimir relinquished the claim at the peace of Oliva in 1660.

So Gustav II Adolf, born in 1594, had never known a time when his cousin was not the bitter enemy. The 30 Years War was both preceded and succeeded by a number of Polish-Swedish wars. At no point in time, at least not after Gustav I's death, were these sons of his just a happy family; but rather engaged in Shakespearean levels of intrigue. In a way the 30 Years War period is the least interesting period of strife between Vasa branches.