They're not going through with it, I'm Saudi and I could write multiple book explaining the very delicate and frail eggshell that is holding my country together, these sentences are carried out by Judges that exclusively follow Sharia Law, but they never go through with it. The problem here lies in one thing, the woman admitted to adultery, even the Sheiks (The judges) persistently advise you against doing that, they repeatedly ask you to repent and hope that Allah listens to you, but they can't keep someone from confessing and admitting to their sin, and so to keep their "integrity" they have to follow the law they claim to follow and sentence her to death. But it's all theatrics, they know they can't go through with it, and they won't. I really wish I could write something a lot more detailed but my English is still a work-in-progress and I'd need to better at it to explain myself better.
And you dare to claim that you are any better than ISIS.
Whole region needs a clean slate. How else do you suggest fixing issues that consistently come up every few years. It won't get any better.