The justice of God is where it has always been: inseparable from God, its Author. Need you be reminded that we have it on the highest authority that God's justice is not like man's?
Your patent desire to spill blood for a transgression that Our Lord Himself responded to with uncompromising disapproval leavened with persuasive mercy is redolent more of Islamic savagery than of an attitude appropriate to a Catholic.
Emperor Charlemagne issued the Capitulatio de partibus Saxoniae upon the Saxons. Capital punishment was used for those who ate flesh during Lent, cremated bodies, withheld themselves from receiving baptism, and showed unfaithfulness to the king. These are relatively minor compared to the heinous crime of adultery. The history of Christendom is filled with countless examples of the secular arm carrying out executions. Do you not believe that adultery causes enough of an offence to God and to society that it merits death?
Capital punishment is a duty for Christian princes to manifest the justice of God and to deter future transgressors.