When you go to another country and openly wage war upon the US, you make yourself a military target. You don't get to wrap yourself in the constitution and enjoy all the procedural protections of the criminal justice system under such circumstances. If Anwar al -Awlaki had felt his life was in danger, he could have just turned himself in to a US consulate and asked for his legal rights.
As for his son, I blame the father for taking him with him to live in an Al-Qaeda stronghold, and effectively using him as a human shield.
The drone strike that killed the kid was targeting Ibrahim al-Banna (and it succeeded in killing him). They almost certainly did not expect that the kid would be there, considering that he lived over 100 miles away far from where that drone struck.
The guy made extensive use of the internet to broadcast his views. Not once did he say 'I reject these accusations and seek a trial/political asylum in some other country.' If you spend all your time glorifying violence and martyrdom, then you can have no complaints when people take you at your word.
There are also legal arguments in favor of this position, but past experiences suggests I'll do a lot of typing and linking to no particular end, so I'll confine myself to quoting Justice Holmes: the constitution is not a suicide pact.
>When you go to another country and openly wage war upon the US, you make yourself a military target.
This is understandable - if Americans are being attacked, their attackers should be killed. Figure out who they are later. But in this case there was no immediate danger. And to steal from Stalin, "how many divisions does al-Awlaki have?" I would love to hear the evidence against al-Awlaki, but sadly the trial was dispensed with, not to mention the subpoena.