Is it permissible for them to use their father’s money when he does not pray?

Praise be to Allah.

Firstly: 

Not praying is a major sin and cause of doom; in fact it is kufr according to the more correct of the two scholarly opinions, as has been explained in the answer to question no. 5208 and 2182. 

The kufr of the one who does not pray leads to numerous rulings in life and after death. Meat slaughtered by him is not halaal, it is not valid for him to be a wali (guardian) or witness in case of marriage, and if he dies he is not to be washed or the prayer offered for him, and he cannot be buried with the Muslims. 

You should carry on calling him, advising him and reminding him, in the hope that he may repent and come back to Islam. See the answer to question no. 47425. 

Secondly: 

The money that he spends on you is not regarded as haraam or impure, so long as he earns it in a permissible manner, such as a job or trade and the like. What is meant by the hadeeth, “Every body that is nourished on haraam, the Fire is more befitting for it” [narrated by al-Tabaraani and classed as saheeh by al-Albaani in Saheeh al-Jaami’ (4519)] is wealth that is taken in haraam ways such as stealing, deceit and so on. 

We ask Allaah to guide you and give you strength, and to guide your father and enable him to repent. 

And Allaah knows best.