The key issue in separation of powers analysis is that of burden. The reason that a republican form of government with democratic institutions has an executive is not because it is virtuous, but because it is practical. It is not possible to have a representative body of "citizen legislators," or even the de facto professional representatives we now endure, set National Park admission fees, order toilet paper for military bases or review research applications at the National Institutes of Health. The executive is there to execute.
The concept of the Constitution explicitly gives Congress such powers as raising taxes and declaring war. The principle underlying such a design is that free people must assume burdens willingly, and the best approximation in a representative form of government is to have those burdens ratified by the representative branch of government.
The president should not impose financial burdens to enable ideological aims or force Americans to bear the strains and sacrifices of battle without the consent of the governed, formalized through Congressional approval. If the executive circumvents this principle, as he has done not only with the military, but regulatory over-reach, and fiscal irresponsibility, it is the role of the representative branch to deny him the resources to do so. That is the remedy. Unfortunately, that takes courage, and we seem to underestimate the importance of courage when we elect our representatives and Senators.