Her husband’s father does not pray because he denies that it is obligatory; how should she interact with him?

Praise be to Allah.

The father mentioned in the question, who does not pray because he denies that it is obligatory, is a kaafir (disbeliever) in the sense of major kufr that puts him beyond the pale of Islam; there is no difference of opinion concerning that among any of the scholars. Such a thing can almost never be done except by stubborn atheists, such as communists and secularists. Whoever denies anything of that which was brought by the Messenger (blessings and peace of Allah be upon him) becomes a disbeliever thereby. If the matter has to do with prayer and other pillars of Islam and its major fundamentals, then that is even worse, because there is no excuse for the one who denies and rejects it, as it is so well known and people grow up in Muslim countries knowing that and respecting it, even those who do not do it. Hence no one would dare to deny that it is obligatory and reject it except one who has gone to extremes in disbelief and stubbornness – Allah forbid. 

Shaykh al-Islam (Ibn Taymiyah – may Allah have mercy on him) said: 

The sin of the apostates is worse before Allah, and in the eyes of His Messenger and the believers, than one who is originally a disbeliever, in several ways. These people are definitely to be executed so long as they do not come back to that which they have left; it is not permissible to make any treaty or peace deal with them or to offer them safety, or to free their prisoners or ransom them in exchange for money or in a prisoner exchange; it is not permissible to eat meat slaughtered by them, or to marry their women or to take them as slaves so long as they remain apostates, according to scholarly consensus. Both their fighters and those who are not fighters – such as old men, the blind and the chronically ill – are to be executed, according to scholarly consensus; that also applies to their women, according to the majority of scholars. 

In the case of one who is originally a disbeliever, it is permissible to enter into treaties with him and grant him security; it is permissible to show kindness to him and to ransom him if he is a prisoner, according to the majority of scholars. If he is one of the People of the Book, it is permissible to offer them protection under Muslim rule, and to eat their food and marry their women, and their women are not to be fought and killed unless they take part in the fighting in word or in deed, according to scholarly consensus. Similarly, none of them are to be executed except those who are fighters, according to the majority of scholars, as is indicated by the Sunnah. The disbeliever who is an apostate is worse in terms of religion and worldly standing than the disbeliever who remains a disbeliever.

End quote. Majmoo‘ al-Fataawa (28/413-414) 

Secondly: 

If the father is as you described him, then we do not advise you to agree to marry his son, unless he will provide you with separate accommodation that is far away from this father. In fact that is the basic and natural requirement: that you should get married and have your own accommodation, separate from his family and your family. 

The fact that the husband is staying in the family home and living with this father as if nothing happened, and as if he has not committed this grave action (of denying and forsaking prayer), cannot be overlooked. Rather he should exhort him to fear Allah and rebuke him for his disbelief and misguidance. Then if he persists in it, he should leave him and avoid mixing with him, and he should protect his wife and children from him, so long as he remains an apostate. 

Please see also the answer to question no. 141680 

And Allah knows best.