Rama's Weakness?

From the start of beginning of The Ramayana, Rama is portrayed as the ideal epic hero for a story. He is obedient, kindhearted, respectful, and he is fully devoted to Dharma. As seen in during the beginning of his banishment, he also cares immensely for his wife, Sita. When she requests to go live with Rama in the forest, he tells her that she must stay in the city where she will be safe. While on the surface this may sound like a good idea, it becomes clear that Rama has in fact contradicted himself in relation to what he told his mother (who had also requested to leave the city to be with Rama in exile). Rama had told her that it was her duty through Dharma that she should not leave her husband. Why then would he tell Sita she had to remain in the city if her Dharma called for her to always be with her husband? The answer is that Rama was madly in love with her, so much that her wellbeing and safety took priority to everything else in his life (including Dharma). It is only when she threatens to kill herself does Rama allow her to come with him into the forest. While girls (and guys) dream about having someone so madly in love with them, this "honorable" trait that Rama displays proves to (in my opinion) be his ultimate weakness. It is not until Rama, Sita, and Laksmana are in the forest that this weakness becomes unmistakeable. This occurs when Sita sees Marica disguised as a beautiful, playful deer and decides that she wants it as her own. While Laksmana correctly predicts that it is in fact a demon, Rama refuses to heed his brother's warning and risks all of their safety in order to get a deer's hide for his wife's enjoyment. As predicted by Laksmana, Sita is lured into a trap and kidnapped by Ravana, and if it weren't for the ridiculous, unrealistic outcome of events that unfold later, she would never have been rescued by her lover. All this to say, Rama's judgement is hindered by his uncontrollable love for Sita. The question remains: is this a weakness or a strength?