Is a young man obligated to go to the mosque for prayer if his father forbids him from doing so and threatens to expel him from the house, also forbidding his mother, because of the mosque's muezzin's reputation?

Congregational prayer is obligatory, according to the preponderant opinion of jurists, and it is not permissible to miss it except for an excuse.

If you predominantly believe that no harm will befall you from your father's threat, then do not miss it; for there is no obedience to a creature in disobedience to the Creator.

However, if you predominantly believe that harm will befall you, then there is no blame in missing it, and you can pray in congregation at home.