cum Romani ab Alba orti essent

Here’s a funny thing…

Haec nuntiant domum Albani. Et bellum utrimque omnibus viribus parabatur, civili bello simillimum, prope inter parentes natosque, cum Romani ab Alba orti essent.

My translation:

They announced this back on Alban soil. And the war was prepared by each side with all strength, most like a civil war, almost between parents and their sons, when the Romans arose up from Alba.

This latter clause '…when the ‘Romans arose from Alba’ alludes (it seems) to the belief that the Roman kings came from a line of Alban kings. I found this out when checking the English translation on Perseus http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0151%3Abook%3D1%3Achapter%3D23. The funny thing is that Orberg’s Latin rendering of this appears to suggest that the Romans arose from Alba as part of the action being described… unless there’s a meaning of ‘cum’ I’m not aware of…?

But hold fast..! unless it’s saying '…it was the nearest to a civil war, almost between parents and their sons, since the Romans had arisen from Alba ?

Yes, “since” is the meaning of cum here.

Cum clauses are circumstantial, with the subjunctive, either causal (“since”) or adversative (“although”); with the indicative (usually) they’re purely temporal (“when”).

Many thanks Qimmik.