Svein II was remarkable in that he had several wives and probably many mistresses.  Not all his children have been documented but this list includes fifteen of the twenty.  Several of the male children became Kings of Norway, Denmark, and Sweden.  The women made connections to other royal families through their marriages and subsequent children and grand-children entered the nobility of the English and French lines. 

Sven had been born in England according to Wikipedia but Skane according to Britannica.  His Danish father was awarded the Earl of England and traveled back and forth between England and Denmark. Unfortunately making a documented history is difficult since much of the information of these early Scandinavians comes from the writings of Snorri Sturluson 1200 or Adam of Bremen about 1100 AD.  This is shortly after the high activity of Viking raids death of Harrald Hardada "Harrald Hard Counsel".

Sven was born, according to most accounts, in present day Sweden.  His father, Ulf af Skane "Thorgilson", had been a Viking through incursion into Normandy, France and England where he was made Earl of England by Knud. After joining forces with his brother he was murdered on orders of Canute I (his brother-in-law) in Roskilde, Denmark. [wikitree.org]

994 - King Svend first attacked England in 994, in the company of Olav Tryggveson (who succeeded in [995] as Olav I King of Norway).  The Anglo-Saxon Chronicle records that "came Anlaf and Swein to London with ninety-four ships and kept up an unceasing attack on the city" 8 Sep 994

Olav I King of Norway attempted to invade Denmark but was defeated by King Svend in a naval battle "inter Sconiam et Seland", during which King Olav was drowned, after which Svend imposed himself as king of Norway

Sven II seems to have had a loyal following among the Danes of the Jutland.  He controlled Hedeby, one of the most important trade centers in Scandinavia.  Unfortunately Harrald Hardada had plans of taking it as his own.  Instead he burns the city down.  Sven decides to battle it out and met Harrald off the coast of Kobenhaven with 300 ships.  He failed to capture Harrald or eliminate the threat.  Sven makes an agreement to not oppose Harrald's rule of Norway if Sven could maintain control of Denmark.  The agreement worked for the most part except that Harrald still felt the need to expand his world and planned the invasion of England.  Harrald did take a substantial army and hundreds of ships to the coast near York.  He had assumed little resistance and was caught away from the ships by English forces, ironically led by one of the sons of Sven II, Eadnoth Fitzharding.  Eadnoth had been a major counsellor to Edward the Confessor and Harold II of England. He met Harrald Hardarda at Stamford Bridge, East Riding of Yorkshire where Harrald takes an arrow through his neck.