First of all, the government is made up of three branches, but they are not exactly "co-equal" in the traditional sense. We often hear people SAY they are, but if you think of this logically, they can't be. Each of the three branches have differing responsibilities and control different aspects, they are not interchangeable or able to fill in for each other, so they are not exactly "co-equal." The Judiciary, specifically, the Supreme Court, is responsible for determining if something is or isn't in adherence to the Constitution. We can argue whether or not this SHOULD be their role, but the fact is, it HAS been their role since the late 1700s--early 1800s. If something is or isn't Constitutional, and the people wish to change that, the Congress has legislative authority to make the change, and the court is obligated to uphold the change.
Now, from a philosophical sense, how can the president be expected to "uphold the constitution" when the court has interpreted it incorrectly? Take for example, the institution of slavery, and every president before Lincoln, who condoned and allowed slavery to persist... were they violating their oath of office by allowing enforcement of an unconstitutional law? Clearly, it is not constitutional to enslave black people, but we did, the courts ruled it was constitutional, and the laws were all based on that precept. Slavery ended with passage of a Constitutional amendment introduced by Congress and passed into law. Once the Constitution was changed, the court could no longer find it constitutional to enslave black people and the presidents who followed Lincoln, couldn't advocate slavery.
Many people believe it is unconstitutional to allow abortion, because it is denying an individual the right to life, clearly outlined in the Constitution. Is the president violating his oath of office to allow abortion? The point I am making is, the Constitution and what IS or ISN'T Constitutional, is subject to individual interpretation of the Constitution. What YOU think is unconstitutional, I may NOT think it is... and visa versa, there is no cut and dried set standard or universal understanding, when it comes to the Constitution... it's why we have entire universities dedicated to teaching about it, it's why we have higher education degrees and diplomas for the understanding of Constitutional Law. It's why we have the Supreme Court! If the Constitution was straightforward and easy to understand, we would never need a SCOTUS to make a ruling on Constitutionality. If we all held the same interpretations and understandings of what is meant in the Constitution, we wouldn't even need to have ANY courts, or law enforcement for that matter... we could all just carry around a copy of the Constitution, and when some dispute arose, we could just whip it out and show the other party where it says what we both understand... no dispute! But that isn't reality, is it? We have case after case, being brought before the Supreme Court, to determine if something IS or ISN'T Constitutional. AND....IF what you are saying is true, the SCOTUS rulings would ALWAYS be unanimous! How can 9 Supreme Court Justices... the smartest people in all the land on matters of the Constitution.... ever find disagreement in something so easily understood and straightforward?