The Rosenbergs were convicted of spying on behalf of the Soviet Union.
No, I think that the sentence was too severe. The Rosenbergs' two sons were orphaned by the executions and were not adopted by any relatives.
One of the sons, Michael Meeropol, wrote The Rosenberg Letters: A Complete Edition of the Prison Correspondence of Julius and Ethel Rosenberg. It recited letters exchanged between Ethel Rosenberg and her sons. In the letters, Ethel felt optimistic that she would be released because of her innocence.