If It Were About Peace …
It wouldn't be called the Cordoba Initiative. The Cordoba Caliphate brutally conquered Spain and ruled most of the nation for over 400 years. "The Great Mosque" was built on the rubble of a Christian church to demoralize the surviving Spaniards. The Mosque still stands today, although it is now called Catedral de Nuestra Señora de la Asunción.
It wouldn't be housed in the same building that fielded the landing gear from one of the planes which was crashed into the twin towers. Or, at the minimum, it would have been moved to a new location in response to the local community's anguish.
It would be a true community center. Instead of containing only a mosque, it would contain at least a small chapel and a temple. These other religious houses, combined with shared common areas, might actually lead to some cultural exchange.
It would openly, loudly, and prominently condemn the medieval doctrine of military jihad and any attempts to inject Shariah law into our legal system. Further, recognizing the equal rights of all, it would provide equal treatment to women rather than forcing them to the back.