Is the son obligated to stop praying in the mosque and suffice with praying at home if his father prevents him out of fear for him, threatening to expel him from the house if he does not comply?

Congregational prayer is obligatory for free, adult men. It is valid anywhere, and the mosque is not a condition for its validity. If your father's fear for you regarding your going to the mosque is merely an illusion, then he has no right to prevent you. However, if you fear the fulfillment of his threat and you are in need of him, then it is permissible for you to pray in congregation at home, and your obligation will be fulfilled thereby, while continuing to try and convince him.