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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is inappropriate for a father to commit such a sin when he is the one responsible for his household and family and is the one who should guide them to good deeds and prevent them from Fitnah (tribulation) and evils. Allaah, The Exalted, says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones, over which are [appointed] angels, harsh and severe; they do not disobey Allaah in what He commands them but do what they are commanded.} [Quran 66:6]
The Prophet, sallallaahu ‘alayhi wa sallam, said: "A man is a shepherd for his family and will be asked about his flock." [Al-Bukhari and Muslim] He should be a role model for his family for doing good deeds, not evil ones.
Nonetheless, all this has nothing to do with the validity of your prayers. If you perform the prayer as due and observe its pillars and conditions, then it is valid. Your father's sin has no effect on the validity of your prayer.
You also bear no sin for the feelings of resentment and hate you have in your heart for your father because of the evil he does, as long as you do not translate those feelings into actions and mistreat or insult him. Islam does not hold us accountable for our involuntary feelings of love or hate.
As for leaving the house, if you want to leave the house because you are exposed to harm or Fitnah, then you should move to another place where you feel safe like the homes of your paternal or maternal uncles whom you trust or the like.
We stress that this father should be given advice kindly and gently and he should be reminded of the gravity of his sin. It is better that the one who advises him is someone who has an influence on him (to whom he may listen). Along with that, you are advised to supplicate Allaah for him; hopefully, Allaah will bless him with guidance to the straight path.
For further benefit, please refer to Fataawa 82882 and 19274.
Allaah Knows best.