Imo He acted in the best manner he could- protecting both his wife and the dignity of the throne he sat on...
some people in Ayodhya were gossiping about the purity of his wife's character... There was nothing he could do about it. ...He cannot shut people 's mouths. ...
He also knows that eventually Sita will also come to hear about the gossip and this was the kind of idle talk which will only increase with the passage of time... Would it do good for Sita, in her state of pregnancy to be listening to what each Tom, Dick and Harry had to say about her character...!!!! Actually ayodhya ppl don't deserve a queen like sita maa...!
And Rama was worried about his pregnant wife...What would unborn child condition in the womb be, if its mother was worried, dejected and upset?...
By sending Sita away... he ensured that she would at least not get to hear the latest on the gossip front. ...
He doesnt abandon her in the middle of no where. He specifically instructs Lakshmana to leave her near Valmiki's ashram, fairly certain that she would be given sanctuary there...