Wagner, Sir Anthony Richard; ‘Pedigree and Progress: Essays in the Genealogical Interpretation of History’
puts this Antipater as the son of Salome and Joseph.
Tal Ilan, in the Jewish Women's Archives http://jwa.org/encyclopedia/article/salome
puts him as the son of Salome and Costobarus
Wagner also suggests that the [Joseph Josephus ., Jr.] who married Olympias (daughter of Herod & Malthace) [Olympias ., the Herodian] was another son of Uncle Joseph [Josephus of Judea (uncle of Herod the Great)] & Salome - rather than the son of Herod & Salome's, full brother, Joseph [Josephus ., Sr.]
Richardson (Herod: King of the Jews, Friend of the Romans) suggests Salome only had children by Costobar:
• Berenice (who first married Aristobulus, then Theudion, Doris's brother)
• Antipater (who married Cypros daughter of Herod and Marriame the Hasmonean)
• unnamed daughter (who married the son of Alexas, Salome's third husband)
The husband of Olympos is given as the son of Herod's brother Joseph
However, Richardson is of course a secondhand source.