Can husband and Wife Or Men and Women cases can be done and ordered through mosque in Islam Like Divorce or adultery? Answer is Yes.
Sahih Bukhari, Volume 1, Book 8, Number 415:
Narrated Sahl bin Sa’d:
A man said, “O Allah’s Apostle! If a man finds another man with his wife, (committing adultery) should the husband kill him?” Later on I saw them (the man and his wife) doing Lian in the mosque.
La-an is that – A man sees his wife committing adultery, but there are no witnesses, and later the woman denies it. Both of them will present their claim to the Qazi, the Qazi will swear to the first man four times that he is truthful and at the end he will say that if I turn out to be a liar, the curse of Allah be upon me. Then, in the same way, the woman will swear four times and say that she is truthful and at the end she will say that if I turn out to be a liar, then the curse of Allah is on me. Then the Qazi will give the decision of separation between them. This is called La-an in islam. In this hadith of the chapter, it was proved correct to decide such disputes in the mosque. The name of the man to whom it belongs was Ao-ymer Bin Amir Ajlani. Imam Bukhari has also narrated this hadith in Talaq, I’tisam and Aqam Muharebeen.