The Courts vs the US President
I was rather shocked to find that it is technically an open question as to whether or not a sitting President can be brought to trial. The consensus appears to be no.
While President, Thomas Jefferson was summoned as a witness in the aftermath of the Hamilton-Burr duel. He refused, writing that if the President could be compelled to appear before the courts, that he would become a lackey to them. Attorneys then negotiated a way for the President to provide the information needed without being summoned by the court.
There have been other cases, but the most recent President to make use of this claim was President Clinton. As mentioned above, the courts have never pressed this issue.
Of course, if the President cannot be compelled to appear before a court, then it is impossible for him to be tried.
The procedure would be impeachment (before the Senate) and removal followed by trial. The really interesting case would be for there to be an attempt to charge him for a crime alleged to have occurred while he was President after he is out of office.
In this case, the function of the Presidency is not directly impacted. OTOH, the problem of political decisions being criminalized would create a precedent that almost no one wants to have.
This is a separate matter from whether or not the President can defy the courts. As mentioned, Jackson did. So did Lincoln. It is interesting to note that in Marbury vs Madison, (https://en.wikipedia.org/wiki/Judicial_review_in_the_United_States) the Court merely declared than a act was unconstitutional. This act was, however, irreversible, so the issue was in fact moot. The Federalist Papers passionately argue that the Court is not bound to enforce or approve laws and acts which it considers to be contrary to the Constitution, but the idea that the Court is somehow the final arbiter as to what is Constitutional is nowhere to be found either in the Federalist Papers nor in Marbury vs Madison.
I expect that the idea would have been preposterous. The expectation was that each of the branches would exuberantly guard its prerogatives, and the Court "controls neither the sword nor the purse." Indeed, if the Court is the final arbiter of what is Constitutional, there is little need for there to be an executive at all. The entire point of having a separate executive is that the courts are not to be trusted 100%. In an egregious case, the executive protects the populace by refusing to carry out a decision by the Courts.
I really enjoyed reading Judge Dredd thirty years ago. But I don't want such a system of government.