(Psst Caddius.... what do you think of the story of Lucretia's rape as a parallel for what prompted Tevinter to come over and sink Arlathan? Before the earliest version of Rome was said to be ruled by "seven kings" - Lucretia's rape by the son of a King prompted them to do away with monarchy altogether!)
The Seven Kings, the later ones being Etruscan, and their overthrow by Brutus and his cohorts (the awesome-sauce Brutus, not his white collar-crime/assassin descendant
) would probably find the most parallels in the pre-Imperium days, from what little we know of it.
Rome and Tevinter have similar starts. It starts off with one tribe, which begins to subdue, through diplomacy and war, the neighboring tribes. And overtime, you've got eighty-seven tribes and are overwhelming Hoover Dam/Pella. (Yes I have been playing Fallout lately, why do you ask?)
I think the nature of ambitious Dreamer mages is what gave Tevinter its' shared power structure, while with the Romans it was in part thanks to the particular tyrannies of Tarquinius Superbus.
So:
Latin Tribes=Neromenian.
Roman city-state=Early days of the Kingdom of Tevinter.
Early Roman Res Publica: Absorbing the other kingdoms.
Post 1st Punic War Rome: Tevinter Imperium being firmly established.
2nd Punic Wars: Tevinter and Arlathan's war. After the war, Tevinter absorbs Arlathan's power and, lacking a rival, quickly expands to cover all of Arlathan's old territories. After the 2nd Punic War, Rome was the power in the Western Mediterranean, and grew in strength enough to challenge the Greek kingdoms battling for control over the Eastern Mediterranean.
My guess for their motivation in overthrowing Arlathan was that it was there, it was powerful, they were the top dog. And Tevinter wanted that power, and thought they had the moxie to beat Arlathan.