We can start it just when she joins forces with Troy, that way it's the best of both before shifting priorities and already working together. Maybe just when she and the people under her command moves in the base that Troy's in charge of, creating unease between the soldiers of both factions that the two leaders could try to remedy. Starting there, Cornelia and Troy could still have those lingering doubts from before they turn sides but also hope for the future now that they found allies and a more unifying goal, allowing their opinions on each other to evolve naturally throughout the story.

I think the aliens would prefer a more subtle take-over, like using mind control a la Geass as their main tactic, especially mind controlling leaders of both factions whenever any attempts of peace are tried by the two sides. Maybe Euphemia being mind controlled is one of the major clues for Cornelia that something else is going on, while Troy could be an expert in tracking down Geass victims and users in the similar vein he is a mage-hunter in his original version. Which would mean more reason for them to team up!