Wagner, Sir Anthony Richard; ‘Pedigree and Progress: Essays in the Genealogical Interpretation of History’

Please see Discussion about whether his wife's name was Cleopatra.

___________

As to Alexander, the son of Herod the king, who was slain by his father, he had two sons, Alexander and Tigranes, by the daughter of Archelaus, king of Cappadocia.

Tigranes, who was king of Armenia, was accused at Rome, and died childless;

Alexander had a son of the same name with his brother Tigranes, and was sent to take possession of the kingdom of Armenia by Nero;

he had a son, Alexander, who married Jotape, (17) the daughter of Antiochus, the king of Commagena; Vespasian made him king of an island in Cilicia. But these descendants of Alexander, soon after their birth, deserted the Jewish religion, and went over to that of the Greeks.

Josephus: Antiquities of the Jews XVIII
Chapter 5 .http://religiousstudies.uncc.edu/people/jtabor/john.html

Alexander

Alexander, also known by his Roman name Gaius Julius Alexander (Greek: Γαίος Ιούλιος Αλέξανδρος, 15 BC-probably between 26-28) was a Herodian Prince.

Alexander was the second born son of Alexander and Glaphyra. His oldest brother was called Tigranes and had a younger unnamed sister. His father Alexander was a Judean Prince, of Jewish, Nabataean and Edomite descent and was a son of King of Judea, Herod the Great and his wife Mariamne. His mother Glaphyra was a Cappadocian Princess, who was of Greek, Armenian and Persian descent. She was the daughter of the King Archelaus of Cappadocia and her mother was an unnamed Princess from Armenia, possibly a relation of the Artaxiad Dynasty. Alexander was the namesake of his father. His name reflects his Hasmonean and Hellenic lineage.

Alexander was born and raised in Herod’s court in Jerusalem. After the death and burial of his father in 7 BC, Herod acted in an extreme and brutal manner returning his mother to Cappadocia, forcing her to leave her children under the sole custody of Herod in Jerusalem. Alexander and his brother remained under Herod’s guardianship so he could be able to control their fates. Another son of Herod’s Antipater, was concerned for Alexander and his brother as he expected them to attain higher station than their own late fathers, because of the assistance Antipater considered likely from their maternal grandfather Archelaus. In the time Alexander lived in Herod’s court, he was betrothed to the daughter of Pheroras. Pheroras was Alexander’s paternal great-uncle and was Herod’s brother. Antipater persuaded Herod to call off Alexander’s betrothal to Pheroras’ daughter because Antipater convinced his father that closer ties between Pheroras and Archelaus of Cappadocia were liable to develop into a plot against Herod.

Herod died in 4 BC in Jericho. After the death of Herod, Alexander and his brother decided to leave Jerusalem and to live with their mother and her family in the Cappadocian Royal Court. After Alexander and his brother arrived in Cappadocia, they disavowed their Jewish descent, deserted their Jewish religion and embraced their Greek descent, including the religion. However the family connections to the Herodian Dynasty weren’t wholly broken. After Alexander and his brother disavowed their Jewish descent, they were considered among fellow Jews as gentiles. There is a possibility that his maternal grandfather sent Alexander to be educated in Rome.

Little is known of the adult life of Alexander. He appeared to an administrator for the extensive land estates in Egypt that were owned by the Imperial family of Rome and he was a wealthy landowner, owing two estates in the Egyptian town of Euhemeria. Alexander married an unnamed noblewoman that flourished in the reigns of the first two Roman Emperors Augustus and Tiberius. His wife bore him a son called Tigranes. Alexander named his son in honor of his brother. Tigranes later served as a Roman Client King of Armenia under the reign of Roman Emperor Nero (reigned 54-68). Roman Empress Livia Drusilla and her daughter-in-law Antonia Minor were mentioned in Alexander’s will.

Source :

https://en.wikipedia.org/wiki/Alexander_(grandson_of_Herod_the_Great)