A family executing the Hadd of Zina if living in a country that does not apply Shari`ah
You are not entitled to execute the punishment; because
execution of Hudud (ordained punishments for violating Allah’s Law) against the fornicator or any criminal, is the responsibility of the ruler or his deputy officers. A fornicator or a person who commits a crime has to repent to Allah and do many good deeds. If the crime involves violation of people's financial rights, the sinner has to give them back to their owners and seek their pardon, be kind to them and pray to Allah for them. If the sinner returns to Allah in genuine repentance and gives people's financial rights back to them, Allah will forgive him out of His Grace and Clemency. Allah (Exalted be He) says,
And those who invoke not any other ilâh (god) along with Allâh, nor kill such person as Allâh has forbidden, except for just cause, nor commit illegal sexual intercourse - and whoever does this shall receive the punishment.
The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;
Except those who repent and believe (in Islâmic Monotheism), and do righteous deeds; for those, Allâh will change their sins into good deeds, and Allâh is Oft-Forgiving, Most Merciful.
(Part No. 22; Page No. 9) Allah also says,
And verily, I am indeed forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them, (till his death).
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.