His father does not pray unless he prays with him – should he pray at home for his sake?

Praise be to Allah.

Firstly: 

Praying in congregation in the mosque is obligatory for men who are able to do it according to the more correct of the two scholarly opinions, as has previously been stated in the answer to questions no. 120 and 8918. 

Based on that, it is not permissible to stay away from praying in the mosque in order to pray with your father. 

But if you pray in the mosque and go back home, it is permissible for you to pray with your father, and it will be a naafil prayer for you, because there is a reason which makes it permissible for you to pray in congregation again. It is proven in al-Saheehayn that Mu’aadh (may Allaah be pleased with him) used to pray ‘Isha’ with the Prophet (peace and blessings of Allaah be upon him) then he would go and lead his people in prayer. Narrated by al-Bukhaari (701) and Muslim (465). 

Secondly: 

You should advise your father a great deal and encourage him to pray and to offer the prayer in congregation. You should tell him of the reports that speak of the punishment for the one who does not pray, and tell him that prayer is the foundation of religion, and the one who neglects it is subject to a warning of a stern punishment, as Allaah says (interpretation of the meaning): 

“Then, there has succeeded them a posterity who have given up As‑Salaah (the prayers) [i.e. made their Salaah (prayers) to be lost, either by not offering them or by not offering them perfectly or by not offering them in their proper fixed times] and have followed lusts. So they will be thrown in Hell”

[Maryam 19:59]

And the Prophet (peace and blessings of Allaah be upon him) said: “Between a man and shirk and kufr there stands his giving up prayer.” Narrated by Muslim (82) and he said: “The one who does not pray ‘Asr, his good deeds will be cancelled out.” Narrated by al-Bukhaari (553). 

And he said: “Do not associate anything with Allaah, even if you are cut and burned. Do not neglect any prescribed prayer deliberately, for whoever neglects it deliberately no longer has the protection of Allaah. And do not drink wine, for it is the key to all evil.” Narrated by Ibn Majaah (4034); classed as hasan by al-Albaani in Saheeh Ibn Majaah. 

It was narrated from a number of the Sahaabah that the one who omits a single prayer deliberately until the time for it has ended is a kaafir – Allaah forbid. 

We ask Allaah to guide us and you. 

And Allaah knows best.