You claimed you didn't want to get into the details as you weren't "qualified" but you seem to be posting alot of the same points from people who want to believe the administration is completely blameless at this. Which is simply not the case. To go over this point by point:
1) Your point on it being "the Judiciaries" role is just plain wrong. Officers of the government, just like officers in the military have discretion about following illegal orders. As evidence: Former Attorney Generals and other people who worked in the Justice Dept. are either speaking out in favor of Yate's actions, or are just not making this argument. At Yate's own confirmation hearing she was asked whether she would follow the law or follow the President's orders if she were confirmed. The people making your argument are the Trump administration, who are the ones on the spot here, and who haven't even been on the job for two weeks yet.
2) "Do foreign nationals who have not yet been granted access to the United States have rights under the U.S. Constitution?"
Yes absolutely they do. Especially if they are being detained by the U.S. government. The Constitution and other laws are more often about limiting what the government can do, then who the government is doing it to.
2a) The people in the initial cases are Permanent Residents of the U.S. They can't get that status removed without some kind of process. And they were being held by Border Protection which brings up direct Habeus Corpus issues.
3) Your point about whether the acting Attorney General should have resigned instead is clearly wrong as well. If following orders does more harm to people than resigning, it is absolutely the correct move to countermand an illegal order. Also, resigning without giving any reasoning just gives the administration cover for their illegal actions, which is more harmful than forcing them to fire you. The only people resigning would help would be the Administration, so ethically, that resigning was not the "right thing" to do.
4) You seem to be confused about the difference between the "Department of Justice" and the "Department of Homeland Security". He didn't consult the Secretary of DHS who was his own nominee on this. And DHS runs Border Protection and a number of other agencies that are the ones enforcing the order. Also, it is typical to consult Congress when you're doing something that might tick off many of our major allies. Especially since Congress was the ones who wrote the immigration act which is at the heart of many of these lawsuits.
5) "It doesn't appear that you've identified a due process that is being skipped."
You mean other than consulting all of the relevant agencies to make sure it doesn't conflict with any laws that cover them, before implementing the change? Consulting Congress before setting up a policy that conflicts with existing immigration law, particularly the Immigration Act of 1965? Setting up an impartial process for green card holders to contest their deportation, which did not happen at all? Giving warning to residents who are travelling abroad that they may have their visa revoked before they leave so they know to put that into consideration? How about setting up a process for the U.S. to continue to meet it's international human rights obligations to protect refugees? Those kinds of things are all "due process" and all actions that you did not cover because the Trump Administration did not do them.