I have no problem with the use of a drone to kill Al-Awlaki. He was at war with us, directing attacks on us.
In modern wars, our enemies have been no respecters of international boundaries, going back to the North Vietnamese attacking us and then retreating into neutral Cambodia. Basically, they play hide-and-seek with us. They come out, hit us, then run into another country, crowing, My goal, 1-2-3! You have to hit them where they are. This is not like when Shelby's brigade, at the end of the Civil War, crossed the Rio Grande into Mexico. They were not dodging into Mexico as a shelter from which they could hit us again. When they crossed into Mexico, they were done.