You cannot be serious. The legal definition of the term "due process" means precisely the opposite of what you are suggesting. Did you possibly mean "due diligence?"
From Mirian-Webster's Dictionary of Law, Due Process is "a requirement that laws and regulations must be related to a legitimate government interest (as crime prevention) and may not contain provisions that result in the unfair or arbitrary treatment of an individual called also substantive due process." You might not like the regulations that govern the no fly list and any other terrorist lists the government keeps and you can challenge them in court as it appears these mutts are doing. If it turns out the process was arbitrary, then they'll get a nice fat settlement. But from what we're told about the nephew and their long stay in Pakistan, it is hard to see what is arbitrary about taking a long, hard look at them.