The Constitution is the supreme law of the land. In other words, the American legal system is subordinate to no other.
As for these murders, despite the fact they are nauseating and disturbing, I do not wish "revenge" upon them. They were afforded due process, were convicted, and were sentenced in accordance with the laws of the land. Just carry out the execution; no amount of punishment or vengeance that could be dealt on this Earth can even come close to matching what God has in store for the killers.
If I had proofread my post prior to posting, I would have caught my pronoun error. I do not wish earthly "revenge" upon the perpetrators of the crime in question. Let God deal with them in the life hereafter.