The primary job of U.S. President is to "faithfully execute the laws of the United States." That's what the executive branch is for. The legislative branch creates laws and the judicial branch interprets laws. While our checks and balances system blurs the lines a bit on the margins and the President has this extra "commander in chief of the armed forces" role, that division is still the primary purpose of each branch.
I don't think there's any question that Donald Trump is not faithfully executing the laws of the United States. He is ignoring the laws he doesn't like. He is refusing to spend money that Congress has passed laws requiring those expenditures. Most of what Trump has done is really intruding on legislative or judicial functions as he issues executive orders that radically reinterpret the laws or the constitution (e.g. birthright citizenship, anti-discrimination laws) or claim to make new law.
I suspect that Trump doesn't actually know what his job is. He thinks President is just the "big boss," without any recognition that he has a specific, and limited, role in the system. He is probably too close minded and/or demented to ever learn what he is supposed to be doing. So really the fault is on the other two branches for not defending their own turf. The current Supreme Court only seems to think that "separation of powers" is when the legislative branch intrudes on an executive function. They have shown a lot less interest in Trump's absurdly unconstitutional claims that he can use executive orders to make laws by fiat.