This is a rarely used law, so the usual disclaimers about it being outside my area of practice and so on apply double
The law is intended to apply to wars and invasions, but I suspect that most courts would largely defer to the President in terms of whether or not a particular set of facts constitutes an invasion (i.e. if congress has not declared war). The gist of it is that courts don't want to second guess a president on matters of national security and tend to say in so many words that "This is an issue involving national security and congress granted the President broad authority to take action, so we're not going to second guess the President, it's up to congress to revise the law if they don't want the President to take action in this situation."
On the other hand, courts are normally hesitant to allow a President to invoke national security and emergency powers as a pretext to make a power grab. The law concerning due process rights of noncitizens has evolved significantly over the years, and a court could hold that Trump's actions violated the due process rights of the prisoners in this case (this would be a way to sidestep second guessing the President on the issue of whether not the Act applies at all).
The final outcome is very unclear to me.
This is back in the news because the judge is holding hearings on whether or not the Trump admininistration violated the court order by not turning the planes around.
A judge will hear arguments Monday over whether officials knowingly violated a court order when they handed over 200 alleged gang members to El Salvadoran authorities.
abcnews.go.com
As a factual matter, it's not entirely clear based on the news reports if the planes landed before the order was issued. If the earlier reports are accurate and the Trump administratoin did ignore the court order, this would be the first example of this that I'm aware of.
President Donald Trump's administration decided to ignore a judge's order to turn around two flights containing alleged Venezuelan gang members, sources said.
abcnews.go.com
The DOJ appears to asserting that the court lost jurisdiction once the planes were over international waters. My initial impression is that this is a weak argument, if in fact it is being asserted.
An undercurrent in many of these cases is that the executive branch (Trump) is asserting that the courts don't have jurisdiction (power) to control actions by the executive branch. Trump is basically asking the courts to declare themselves powerless. This is obviously not sitting well with many of the Article III federal judges, but I could imagine this Supreme Court castrating themselves in a harakiri-like display of loyalty to Trump.
But, back to the disclaimers, I'm not an expert in this area of the law and I have not researched the issues.
