I haven't been following this thread so I may be repeating someone.
First (leaving aside how courts act in practice) international law has a firm basis in the Constitution of the United States. Look up the aricle on the status of treaties. International law does not consist (in principle and sometimes in practice) merely of general principles but is embodied in treaties negotiated and ratified by some or all nations. Once a treaty is ratified by the U.S. Senate, in principle (and sometimes in practice) a citizen of any nation may bring suit in u.s. courts and win damages for harm done by (e.g.) the USAF in actions contrary to this or that treaty.
It doesn't happen very frequently, but it does happen. Courts usually follow politics rather than law or constitution, but that is another issue.
Intgernational Law IS real law, not just principles. That is the starting point for discussion of it, though that discussion needs t go on to consider the enforcement of it, the use of it for agitational purposes, etc.
Carrol