Is he who prays alone at home, due to his inability to hear the call to prayer, even though the mosque is close to his home, sinful; or is it obligatory for him to pray in congregation at home?

Scholars have differed regarding the ruling on congregational prayer, whether it is an individual obligation (fard ayn), a communal obligation (fard kifayah), or a confirmed sunnah. According to the view that it is obligatory, it is incumbent upon whoever hears the call to prayer. If your going to the mosque will lead to your family becoming negligent in performing their prayers individually, then it is better for you to lead them in congregational prayer at home.