No. As far as the repentance gate is open for every one as we read in Quran, we can never claim that a person who committed a sin is a permanent sinner. As a witness of his committing the sin in front of you, you need to verify whether he is still committing sins or not before praying behind him. You are not allowed to tell others not to pray behind him nor inform them about the sin which you witnessed unless he did it openly with out caring to public seeing him committing the sin.
General Salatul Tawbah is just two Rak'ats like Morning Prayers, which can be performed any time during the day or night.
'There is a special Salatul Tawbah during the month of Thul Qa'dah which contains two then another two Rak'ats. It is performed on Sunday after performing Ghusl. Every Rak'ah has one Sura Al-Hamd then three times Sura Tawheed, then one time Sura Falaq and one time Sura An-Naas. After the prayer to recite seventy time ASTAGHFIRULLAH, then say one time LA HAWLA WALA QOWWATA ILLAHVBILLAH AL-ALIYYIL ADHEEM.
It is wrong for your wife to pry into your past sins, and if it has nothing to do with your current life or has no involvement with your marriage, it is haram for you to disclose it to others. We are not allowed to expose our previous sins to others, or confess to anyone about the past, especially if we have repented.
She should refrain from asking you about it, and you do not need to lie. You just refuse to give any information about it.
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