I can find no sources that suggest that Herod the Great's mother, Cypros /Kypros /Kufra, of Nabatea is a daughter of Aretas III, King of Nabataea.
All sources appear to say is that she was the daughter of a noble Nabatean family. Herod the Great, de-facto King of Judea is said to have tried to seek refuge with Malichos I, King of Nabataeans - a cousin? - who turns him away: cf https://en.wikipedia.org/wiki/Malichus_I
This doesn't seem to me to be proof enough of Cypros's father being Aretas III, even though the relationships seem quite likely, given that Herod the Great's son, Herod Phillip Antipas ., Tetrarch of Galilee and Perea married Aretas IV Philopatris, king of Nabataea 's daughter, Phasaelis ., of Nabataea.
It looks too much like someone played convenient join the dots with the only profiles we have. Cutting, pending Sources - which may well come with clearer sources to link the family relationships between the Nabatean kings: https://en.wikipedia.org/wiki/List_of_Nabataean_kings
Herod the Great, king of Judea is Raúl Castro Chacón, Capitán de Navio's first cousin four times removed's wife's 63rd great grandfather!
Raúl Castro Chacón, Capitán de Navio
Tú → Raúl Castro Puga
your father → Aurora Puga del Valle
his mother → Raimundo Puga Puga
her father → José María Puga Sepúlveda
his father → José de Puga y Figueroa
his father → Rosa Camila Puga Córdoba Figueroa
his sister → Francisco Javier Cajigal del Solar y Puga
her son → María Josefa Vial del Campo
his wife → Francisco Diego Vial Santelices
her father → Manuel José Jose Vial Jarabeitia
his father → Francisco Manuel Vial Ondarra
his father → Andrés de Vial Barallón
his father → Francois de Vial y Savoie
his father → Françoise de Savoie
his mother → Emmanuel Philibert I, duc de Savoie
her father → Charles III 'le bon', duc de Savoie
his father → Philippe II "Sans Terre", duc de Savoie
his father → Princessa i Cypren, Duchessa di Savoia Anne d'Savoie
his mother → Janus, King of Cyprus and Armenia
her father → Jacques I, King of Cyprus
his father → Alix d'Ibelin
his mother → Guy d'Ibelin, Sénéchal de Chypre
her father → Alix de Lampron
his mother → Hetum Iv Lampron
her father → Constantine I "the Thagadir", Prince de Lord of Lampron, I
his father → Hetum III, Lord of Lampron
his father → Oshin II, Prince of Lambron
his father → Zabel Rouponi
his mother → Toros II Rouponi
her father → Levon Rouponi
his father → Konstandin Rouponi
his father → Eudoxia Bagratun
his mother → Gagik II, king of Armenia
her father → Ashot IV, king of Armenia
his father → Gagik I "the Great" King of Armenia
his father → Ashot III of Armenia
his father → Abas I, King of Armenia
his father → Smbat I "the Martyr" King of Armenia
his father → Ashot "the Great", King of Armenia
his father → Hripsime Bagratid
his mother → Ashot I "Msaker", King of Armenia
her father → Adarnase Bagratouni, Prince of Armenia
his father → N.N, Daughter of Ašot III Chosroide
his mother → Ašot III, Prince of Armenia
her father → Smbat VI, King of Armenia
his father → N.N. Arshakuni
his mother → Manuel Arshakuni
her father → N.N., son of Johannes Moustakon
his father → Placidia
his mother → Flavia Juliana
her mother → Flavia Proba
her mother → Eirene
her mother → Flavia Magna
her mother → Maria
her mother → Petronius Maximus, Roman Emperor
her father → Anicius Probinus
his father → Sextus Claudius Petronius Probus
his father → Petronius Probinus
his father → Anicia Demetrias van het Romeinse Rijk
his mother → Amnius Anicius Julianus
her father → Sextus Anicius Faustus Paulinianus
his father → Asinia Juliana Nicomacha
his mother → Gaius Asinius Nicomachus Julianus
her father → Gaius Asinius Quadratus Protimus
his father → Julia Quadratilla
his mother → Aulus Julius Claudius Charax
her father → Julia Quadratilla Bassa
his mother → Julia Iotapa
her mother → Gaius Julius Alexander ., King of Cetis
her father → Tigranes VI, King of Armenia
his father → Caius Julius Alexander ., II, of Judaea
his father → Alexander, III, Prince of Judaea
his father → Herod the Great, king of Judea
his father