You know a lot can be said about deficiencies in the democratic process in the U.S. but the crazy guy would just be removed. He'd need decisive support from the military to stay and ride out the fact that he lost all democratic legitimacy. I don't see a coup on the horizon. Do you?
I'm going to go out on a limb and say that Trump's actions that you imagine to be constitutional violations are probably actions that you personally disagree with, but are not actually constitutional violations.
Republicans as a group care deeply about the Constitution, and the Constitution is clear about when the term of the presidency ends. He would not have the support of the Republicans in the Senate if he chose to remain in office past the expiration of his term.
> Republicans as a group care deeply about the Constitution
Well, they say that a lot, I can't see any evidence that it's particularly true in general (it's definitely true that there are things that they care about that they cite their particular interpretation of the Constitution to support, though on issues like executive vs. legislative power their deeply held Constitutional beliefs seem to flip 180° when you flip which parties are in power in the respective branches; the Constitution seems to be more of an identity touchstone than a document whose actual content is of particular concern.)