One thing I would like to correct people on...Ram never asked Sita to jump into fire. According to Valmiki Ramayan, he simply told her to go where she pleased, because he had fulfilled his Dharma in rescuing her from Ravan's clutches. Sita then ordered Lakshman to kindle a fire so that she could jump into it, because she could not conceive going anywhere where Ram was not present. Agni Dev then appeared and proclaimed Sita's purity to all, and Ram accepted her back.
According to Valmiki Ramayan, Ram himself never asked Sita to jump into fire.
According to Tulsidas, the Sita Ravan had abducted was not even the real Sita. She was the shadow form of the real Sita which Ram and Sita had concocted to fool Ravan, and so in this version when Ram asks Sita to give an Agni Pariksha, it was to regain his real wife who had been safeguarded with Agni Dev the entire time. The shadow form of Sita was gone during the so-called "Agni Pariksha" and the real Sita returned with Agni Dev. Only Ram and Sita knew of this, and eventually Lakshman, but to the entire world it looked as if Ram had asked Sita to proove her chastity.
As for Sita's abandonment, we must remember that Shri Krishna himself said for the sake of a household, one member must be sacrificed if necessary. For the sake of the town, one house, and for the sake of the country/kingdom, one village. It is the King's Dharma to consider his praja above all else, even his own family, and if their betterment must be wrought by sacrificing a member of his family, that is his duty to do so. Sita was not at fault for this, but it had to happen for Lok Kalyaan. We can draw a paralell with Krishna's sacrifice of Pradyumna. He allowed his infant son to be kidnapped by Sambhrasur because Pradyumna had to eventually kill him. What was the infant's fault? One can say the baby was even more innocent than Sita Ma, and did not deserve to be separated from his mother and father at such a young age. As a father, was it not Krishna's Dharma to protect his son and prevent the demon from kidnapping him? Yet Krishna knew he had to sacrifice his son for the sake of Lok Kalyaan, and likewise, despite Ram's duty to stick by his wife as a husband, his duty as a King was higher in that case because it affected his people. Both Sita and Pradyumna cooperated in both cases, because they too knew it was right. Sita herself never rebelled against Ram during vanvaas, and she brought her children up to respect their father. That is because Sita knew her duty as Queen of Ayodhya, and she knew it lay in the betterment of the people.
Dharma is not rigid. It does change for every circumstance and situation. People have many Dharmas, that of a child, parent, spouse, ruler, etc, and we must use God's avatars as guidance to determine which Dharma takes precendence in a particular situation.