The president names the agency heads, and their mandates expire roughly or exactly at the same time as the president's. That's more than enough control. The president can't and shouldn't then go and get into the weeds of specific policies that those agency heads then coordinate.

Also, settling the ultimate interpretation of the law is indeed the prerogative of the courts. This has actually changed quite recently in some ways - the SC has recently struck down the Chevron Doctrine, which held that the courts would defer to the executive when a law could be interpreted in different ways. So right now if Congress passes a law that says "the EPA shall insure that American citizens have potable drinking water", it is ultimately up to the courts to decide if the level of lead in water set by the EPA makes the water potable or not.

But however you slice it, the president shouldn't be the one to decide if the level of lead in water being enforced by the EPA is too little or too much. If the head of the EPA and the courts believe that a certain level is good enough, than that's that. After all, the president chose this head of the EPA. The next president can choose another head.