Cleopatra of Jerusalem - Could Herod have had a child with Cleopatra of Egypt?

I've come across a Wikipedia mention of the possibility that Herod's wife, Cleopatra of Jerusalem, might actually have been an affair with Cleopatra of Egypt.

My urge is to discount it completely, but the source cited is Josephus:
"However, it is also possible that Cleopatra of Jerusalem really was Queen Cleopatra VII of Egypt. Josephus mentions "Cleopatra of Jeruslaem" twice: once in Antiquities 17.1.3 and once in War 1.28.4. It is interesting to note that according to Josephus, Cleopatra VII and King Herod became intimate, and that Cleopatra "upon the whole, seemed overcome with love for him (King Herod),"(Antiquities 15.4.2). Herod is said to have had a son named Philip with Cleopatra of Jerusalem while it is believed that Cleopatra had a third child with Marc Anthony also named Philip. It is during Marc Anthony's absence that Cleopatra, according to Josephus, spent a great deal of time with King Herod." http://en.wikipedia.org/wiki/Cleopatra_of_Jerusalem

Now at first glance this seems highly unlikely, just given the documented extent of their dislike for each other, and, as http://www.geni.com/people/Justin-Swanstr%C3%B6m/6000000007278581048 points out, most of these 'conspiracy theorists' seem to forget how few names circulated amongst the people of that time. Hundreds of people in the historical records were called Mariamne, Salome, Joseph for example. So, two Cleopatras who knew Herod do not constitute evidence of one person.

But then you start to think about how she typically used sex to get political power, and you wonder if it might just have been sufficiently economically expedient for her to manipulate Herod this way.

I'm finding no quick internet back-up for this though. And even the two biographies of her I've got on my bookshelf ignore Josephus's apparent statement that Cleopatra "upon the whole, seemed overcome with love for him (King Herod),"(Antiquities 15.4.2).

Curioser and curioser...