It's called "the supremacy clause" of the United States Constitution.
That's not all. Art. 2 is about the President.
Were any U.S. president ever caught ceding authority to the U.N. they'd be subject to impeachment for purgery; violating their oath, and their sworn duty.
Bush (both) got U.N. approval before their Middle East wars.
But that's a fig leaf.
In the United States of America, no law trumps the United States Constitution.
PS / note:
If you closely examine Art.2 Sect.1 part7, you will see "... so help me god" is NOT any part of the Constitutionally stipulated oath.
Yet presidential inaugurees have been prompted for it for as long as I can remember.
That's not correct. Bush Junior didn't get approval from the UN Security Council but decided to force the issues on Saddam, through a US pre-emptive war policy, by attacking Iraq despite objections, in particular from Germany, France and Russia. As we all know, the main reason for the attack was the threat against US sovereignty from Iraqi WMD which the Inspectors never found at the time and were never found after the war either.