Question: Who is the mother of Pompey's children? His new wife can't be their mother, since they are too old compared to Niobe's son who's an infant when the show starts. And they can't be Julia's children, since Pompey is worried Caesar might kill them, and Caesar wouldn't murder his own grandchildren.
Question: I don't understand why Pullo is so angry with Vorenus and thinks he needs to apologise. Having fought in Caesar's army for as long as Pullo has he would be very well aware of the repercussions for what he did, why would he blame Vorenus for abiding the law and doing what is required of him as a centurion?
Answer: Its Pullo's nature to resent people of higher standing than him. His jealousy of Vorenus in later episodes, which in part leads to their falling out, is proof of that. From Pullo's point of view, Vorenus just got better breaks to get where he is in the army and so, isn't really his superior. That, plus his natural arrogance is explantion enough for his behaviour in spite of the fact that he broke the rules and was being fairly punished.
Answer: According to wikipedia, Pompey's children are all from his third wife, Mucia Tertia. Julia is his fourth wife. See: http://en.wikipedia.org/wiki/Pompey#Marriages_and_offspring.
Myridon