To Ram, it was Raj Dharma or Royal dharma. From the moment he had promised Kaikeyi, whom he addressed as 'Ma', through out his life, that he would go to forest wearing 'valkal', un-dyed coarse cloths fit for 'tapasvins' and 'sanyasis', living like one of them for next 14 years, to the moment he asked his father to bid him farewell, he had told everyone that he needed to do this as that was his Raj Dharma.
To Sita, it was Stree Dharma or Womanly dharma. From the moment Ram decided that he would go to forest to live like a hermit for next 14 years, Sita decided to accompany him. She was forbidden to so even by her husband whom she wanted to accompany and other family members. But she calmly said that she needed to this as that was her Stree Dharma.
Now Ram, who was a dutiful son to his father and responsible son to his mothers(Kaushalya, Kaikeyi, Sumitra), why chose to fulfill only one of his mother, Kaikeyi's wishes and refused to listen to his father and other two mothers Kaushalya and Sumitra? Wasn't that his duty to listen and obey his father's wish? Wasn't that his responsibility to fulfill his own mother Kaushalya's wish? While Kaikeyi wished for Ram's forest exile for 14 years as hermit, Dasharath, Kaushalya and Sumitra wished him to stay with them whether he would become a king or not. But Ram not only rejected his claim over the throne, he readily agreed to go to forest for next 14 years. The reasons for his actions were: as a king, his father Dasharath, was bound to fulfill his promises given as boons to Kaikeyi, as that was the way and traditions of Raghu clan and very foundations of Ikshavaku clan. But Dasharath had failed to keep up his role and dharma as king when he went back to his words and refused to consider Bharat as a king. His refusal irritated and infuriated Kaikeyi so much that she had to throw her queenly tantrums to bring Dasharath into her quarters while Ram's coronation ceremonies were going on, and demanded her rights, her boons from the king Dasharath right away. A king should be a example of ideals and principals. But Dasharath's behaviour was unfit and improper for a good king. So Ram, who was born as a prince into the Royal family of Ikshvaku and Raghu, which was known for its steadfastness and keeping up the given promises, chose to follow the duty and responsibility he had as a prince. Because in the ever changing world and nature, as Ram, his truth would be always the eldest prince of Raghu clan. And as prince, he not only had to protect and serve his all subjects but also he had to keep up the family reputations and its traditions, as it was the Raj dharma. And the Raj dharma demanded him to fulfill Kaikeyi's 2 wishes and went to forest for next 14 years.
Sita, she was given into the marriage to Ram, the eldest prince of Raghu clan. She was a dutiful wife and responsible daughter-in-law. Yet she unheard his husband and his father-in-law and all mother-in-laws. As wife, her duty was to listen and comply with Ram's wishes but she wore the 'valkal' meant for 'sanyasis' and 'tapasvins' against his consent. Her responsibility as daughter-in-law was to serve and take care of her in-laws yet she chose the forest exile for 14 years instead. Weren't all of these contrary to her dharma as wife and daughter-in-law? Her reasons were: Stree dharma. Sita, born out of nature, out of the Earth, was a woman in the ever changing world and nature. This was her truth which she couldn't deny. So when Kaikeyi, also a woman, asked her son ,Ram, whom she claimed had loved the most, to go to forest and secured the throne for her own son Bharat, showed how blind she became in her frustration and her anger. She was repeatedly rejected from her husband, Dasharath, whenever she reminded him his promise given to her father, king of Kekaya, of making Bharat the king, instead of Ram, during her marriage. She became selfish and behaved like a jealous and horrible step mother, instead of affectionate and patient mother. She failed to keep up her Stree dharma, when she knowingly hurt her husband, two other queens and wives of Dasharath who were like sisters to her and all of her family members. This shouldn't be the way a woman, a queen should behave. So Sita chose to go with Ram, not out of obligations as a wife but as a woman, to uphold the Stree dharma, as was the demand of the time, to exemplify what it is to be a woman, how it is to be a sister, a wife, a daughter.
Ram and Sita both chose to uphold the dharma, according to their own, their Swa-dharma. For Ram it was Raj dharma and for Sita it was Stree dharma...And with their own respective swadharma...the very foundation of dharma has been made of, which carries the essence of humanity and its potentials.