Not that it will make you feel much better, but keep in mind, this is civil law for God's chosen people, the Hebrews, whom He was raising up to be peculiarly His own, from whom would spring the Messiah. They had special, strict rules that was necessary to set them apart from the paganism of the surrounding peoples.
Its interesting to note that in the OT, the ten commandments were kept in the ark of the covenant. On the lid of the ark was something which is known as the mercy seat. One must pass by the mercy seat to get to the Law. The law is always harsh and uncompromising and this is the nature of a rule or law. It is unbending and the results of breaking them are like reflex actions or pushing the button on a machine. It is unthinking and has no compassion but it merely acts. I believe there is a high level of significance in this, and am very thankful that the mercy seat comes before the Law. The mercy does not nullify the Law, but it covers and protects the recipient.
Ok, I am no expert in this area, but I do know that mercy plays a role in the implementation of these harsh rules. If there is no rule, then grace is not needed or appreciated. The standard has to be there, so that even though to extend mercy is desired, the recipient has to be aware of the standard, and thus, aware of the amount of grace that has been extended to him/her. Repentance seems to also be necessary for mercy to be extended. The presence of the rule or law, coupled with a truly repentant heart of the recipient, has the function of pulling that person back into line with the desired behavior which is the bottom line at the end of the day. In the story of Jonah, he was commanded to go to Ninevah and tell them their city was about to be destroyed, but apparently this was subject to change, because when the city repented, God relented and did not destroy the city. One could make the argument that God broke his Word then, but apparently His wrath is based on a continuing in wrongdoing and can be assuaged by a turning from the sin. Even the OT says that God is slow to anger and quick to forgive. Having said that, He is, by His very nature, the source of all justice, and therefore, in order for Him to forgive, there had to be the eventual payment of this sin debt. I'm sure you know where I'm going with that, and that is a whole other thing, hard to understand.
As harsh as it seems, it is also worthwhile to note that Yahweh is equal opportunity when it comes to sexual sin. Those caught in adultery with those of the opposite sex were also commanded to be stoned.
After saying all that, it occurs to me I haven't really answered your question. The thought of stoning someone is not appealing to me at all. I hesitate to ever say what I would do in a given situation, but I can only say it is always right to follow what Word of the Lord is, assuming you're listening to the true God who cannot do wrong.