Answer:
Ram and Sita, being Vishnu and Lakshmi respectively in human form, both know that the other is chaste. Ram believes Sita when he reclaims her from the walls of Lanka. If you have seen Luv Kush, this is when they go more in depth into this story. The public, knowing that Sita spent around a year or so within Lanka's walls, accused her of disavowing Ram and not being chaste anymore with the former King of Lanka, Ravan. Due to this, Ram, as the King of Ayodhya, had to follow his Raj Dharma, which necessitated Sita leaving the palace once again. He did not want her to leave, but it was actually Sita's decision to save her husband's good name that lead her to leave of her own will, still knowing that she is chaste and that the public was false accusing her. Hope this helps.