I don't believe it's anywhere suggested that Thorongil was "the Steward's right hand," or had any status except as a military captain, and there's no particular reason to suppose that he would have visited Dol Amroth or met the Prince's toddler; his job was with the Army and the Fleet.
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The entire plot of The Lord of the Rings could be said to turn on what Sauron didn’t know, and when he didn’t know it.
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