In Conclusion...
When Hal says he has the backup of the Doxon Duchy, he is not just referring to his mother and she was actually the least he was referring to in that statement.
The entirety of the Doxon family, except his grandfather and his mother, was under his control.
The Elders might not know it but Hal was not just the son of the one who controls the Duchy but was practically in control of the Duchy by himself.
A Duke in all but name.
"So now that we have ruled out execution..." Hal began but he was quickly interrupted by one of the Elders who said,
"We have not ruled out anything," he said.
Hal waved his words off and said,
"No, we have. Let us not continue to discuss the issue as that would be quite embarrassing for you and quite frankly, it will be pointless.
Now, on the matter of your proposed, nay, your only punishment for me; turning me into a Pseudo-student.