Lord Ram is the Divine Incarnate, the perfect man and perfect Divine Being. When he made that decision he was not questioning the purity of Sitaji. He acted as the King for his subjects and not as the husband. It was his duty to address the doubt that had arisen in the mind of his subjectss, to show them and to prevent unrest in the minds of the people. It is something like a judge who has to rule on his own son in court. At that moment, he has to play the role of a judge because he is in that position and rise above his personal feelings. Lord Ram sacrificed the personal, for the sake of the greater good. Lord Ram was simply abiding by his Dharma. And the action came from that space of impartiality. He is an example to us that we must always put purpose before our self.