“Rights of a defendant in a criminal felony jury trial? When a defendant goes to trial on a criminal felony and the jury comes back deadlocked? With a verdict of 9-3, can the judge make them go back and deliberate again after they announce the verdict in the courtroom?”
A verdict is by definition, unanimous. Thus, 9-3 (in a criminal matter) means the jury is deadlocked or undecided. The judge absolutely can and will have the jury go back and deliberate further unless or until he or she is satisfied that there is no reasonable likelihood the jury can agree. If the jury stays deadlocked, whether 9-3, 8-4, 6-6, 11-1, and there is no way the jurors will come to a verdict, then we have a hung jury. A hung jury is typically a win for the defense even though the case starts all over (this is true for many reasons I can explain if you are interested). Note, that a defense lawyer should pop up and move for a mistrial as soon as it becomes reasonably clear that the jury is deadlocked even if the judge denies and keeps the jury in. Judges do not want a hung jury mistrial because they want the case to resolve itself and be over in one way or another (whether by virtue of acquittal, settlement, or conviction). This is why you may be seeing or hearing the judge pushing the jury to deliberate further despite the fact that the jury has already written the judge that they are undecided.