Is it permissible to pray behind two imams who make mistakes in reciting Al-Fatihah, and what is the way to convince my father to pray at home given the situation?

May Allah increase your father's eagerness for good deeds. Congregational prayer is one of the greatest acts of nearness to Allah. As for imams who pronounce the letter "ض" (ḍād) as "ظ" (ẓāʾ), many scholars have made concessions regarding this issue due to the proximity of the two letters' points of articulation and the difficulty of avoiding this mistake. There is no harm in adopting this view. However, if someone makes a grammatical error that alters the meaning, then prayer behind him is not valid. Therefore, if you are praying behind someone whom it is valid to follow, then obey your father and pray in the mosque. But if you are praying behind someone behind whom prayer is not valid, then you must repeat that prayer, and it is better to pray at home.