All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There is no doubt that the husband is religiously required to treat his wife kindly as Allaah Says (what means): {And live with them in kindness. For if you dislike them, perhaps you may dislike a thing and Allaah makes therein much good.}[Quran 4:19]. Moreover, it is confirmed that the Prophet said: "The best among you are the best (when dealing) with their wives." When some women complained about the bad treatment of their husbands to the Prophet, sallallaahu ‘alayhi wa sallam, he, sallallaahu ‘alayhi wa sallam, said: "Those (husbands who mistreat their wives) are not the best among you." [Ibn Maajah].
We have already issued Fataawa 90751 and 89630 clarifying the stand of the children towards their father if he mistreats their mother, so please refer to them. We have also issued Fataawa 89109 and 87877 clarifying the ruling of a spouse having doubts about his/her partner, so please refer to them.
As regards your question whether or not the prayer of your father is accepted if he mistreats your mother, then the answer is that the prayer has some conditions and pillars and if one fulfils them, the prayer is sufficient and it is hoped that it will be accepted. However, it is not possible to authoritatively assert that someone's prayer is accepted, because this is a matter of the unseen which can not be known except by revelation and the revelation stopped. However, it is feared that a person who has a bad conduct would enter Hellfire as the Prophet replied when he was asked about a woman who performs the prayer abundantly and fasts regularly but she harms her neighbours: “She is in Hellfire.” [Ahmad].