Uttar Kanda is not part of Orignial Ramayana. It could have been written by one Tamilinan like you. Regarding Killing Vali, it was a punishment to Vali. At that time, any person, who stole his brothers wife was awarded Death punishment, which is even existence in Muslim Countries even now. Rama being a representative of King, awareded the punishment. Rama never doubted his wife Sita. If you read Original Ramayana (Valmikis, not a tamil aethist Ramayana), you would realise it. He banished her to maintain the High Standards of a King, which your cm can never follow ( He should have handed over his son for burning people in a press, he chosed to close his blind eyes).