Is it permissible for someone who has prayed the obligatory prayer to repeat the prayer with his father in the mosque or alone? And which is better: praying with the father or in the mosque?

First: Congregational prayer is obligatory for able-bodied men in the mosque. Therefore, it is not permissible to abstain from it to pray with your father. However, it is permissible, after praying in the mosque, to pray with your father, and this would be a supererogatory (nafila) prayer for you.

Second: You should frequently advise your father and encourage him to pray in congregation, and explain the punishment for neglecting prayer, based on the Almighty's saying: "Then succeeded them a generation who neglected prayers and pursued passions; so they are going to meet Ghayyā" (Maryam 19:59), and the Prophet's (peace be upon him) saying: "Between a man and polytheism and disbelief is the abandonment of prayer," and his saying: "Whoever abandons the Asr prayer, his deeds have been nullified," and his saying: "Do not intentionally abandon any obligatory prayer, for whoever intentionally abandons it, the protection of Allah is lifted from him."