Correct: the Jews knew they could use Caesar's laws to get what they wanted and have the innocent Son of God tortured and executed. The Jews would have had Pilate executed for not following the laws and then the Jews would have had Jesus Christ tortured and executed anyway.
But at the end of the day, Pilate chose to save his own skin and not get in trouble with Caesar rather than let an innocent man go free.
Correct: the Jews knew they could use Caesar's laws to get what they wanted and have the innocent Son of God tortured and executed. The Jews would have had Pilate executed for not following the laws and then the Jews would have had Jesus Christ tortured and executed anyway.