You have no problem with AMERICAN CITIZENS BEING EXECUTED AND HAVING THERE RIGHTS VIOLATED?
The question is at what point is it no longer possible or practical to treat US citizens waging war on their country in the service of a foreign enemy the same way you'd treat a US citizen who commits a crime at home. Personally I think every effort should be made to arrest them, after which they can experience the benefits of our judicial system. But if that's not possible because they are protected by a foreign country, for example...what do you do? I'm not sure that applied to any particular situation, but it's worth thinking about. Drones give us a kill capability far above our arrest capability (and arresting was always the harder option anyways).
Personally I don't think it's a simple question with a simple answer. I don't like the idea of the President being able to kill a US citizen without a fair and impartial trial and all that. But I also don't like the idea of a terrorist being able to get away with waging war against the United States because we can't practically capture him and can't legally kill him.
Like I said though, I'm not entirely convinced we've actually faced this situation before. The actions of President Obama in this regard should be considered differently from the underlying question.