As we know the purpose of Rama avatara was to liberate Ravana, and for this purpose Vishnu had to forget his divinity. But in the Yuddha Kanda, after the Agni Pariksha, all the devas headed by Brahma arrive and praise Rama reminding him of his Divinity. They tell him that he is Vishnu and Sita is Lakshmi. You can read the praises of Brahma here
After this Rama becomes the King of Ayodhya. So now did Rama rule with the knowledge that he was Vishnu or did he forget it again? That is did Vishnu sit on the throne of Ayodhya or Dasaratha's son?
And similarly was Sita sent to the forest where she lamented her fate to Lakshmana - or did Mahalakshmi lament to Anantadeva?