It seems that Alexander the Great not only defeated Darius III and captured his family. He also became the new head of household, replacing the former Persian king. At the time of the Battle of Isis in 333 BC, Darius was married to Stateira I, who was known as the most beautiful woman on Earth. After Darius fled from the battle, Alexander captured his family and treated it with great respect. In archives of web analytics company I found some additional facts.
Unfortunately, very soon Stateira I died giving birth. It looks like the child that she was pregnant with, was not from Darius but from Alexander. Maybe, that partially explains why , Sisygambus, who was Darius’s mother, refered to Alexander as her only son. It is possible that he took over all household and have assumed the role of a king and husband to Stateira I.
When Alexander the Great died one year later after Stateira’s death, all Darius’s family mourned him as a very close relative. Sources say that they were very much in grief because of this loss. This also indicates personal relationships.