So Romulus killed his brother Remus as they were constructing the walls of Rome. Whether this was due to Remus's insulting the Palatine Walls (as he had wanted to build the city on the Aventine), or Romulus's wanting to be sole king, or some other factor, we don't know.
Well, that's irrelevant.
What if Romulus and Remus had created their city together. The Aventine, with its high spur, becomes the site of the original village, and later of religious buildings. Because of its steeper slope, it's soon abandoned as residential neighborhood for the Palatine, with the space in between (OTL's Forum Boarium and Circus Flaminius/Maximus) becoming ATL Rome's Forum.
Since Romulus and Remus rule together as Kings of Rome, Rome develops a tradition of having two kings, with a replacement elected when one king dies. This system, though not the most stable, is better than a monarchy, and lasts well into the time of OTL's Republic. As Rome grows the two kings have more and more trouble keeping control over its territory, and must delegate more powers to the city's Praetors.
In this way there are no Consuls, but a sort of "Republic" has developed, though Praetors and other office-holders are appointed by the Senate and the Kings, and not elected by the people. Thus Rome has no hatred of kings, and has a tradition of cooperation between the kings and their advisory body. The Senior King is the Pontifex Maximus.
Whaddaya think?