I need your advice on how I should handle my problems with my father.
I am a young man who follows the Salafi manhaj and still lives with his parents. Although he prays, my father is a disobedient Muslim: he does not pray in the Masjid and rather watch TV and pray at home when he feels like it. He does not ordain his daughters, which are my sisters, to observe proper Hijab and does not forbid them from intermingling with men either in school or at work. He even let them kiss my adult cousins, which are not Mahrams, in the cheeks. I came to the conclusion that my father is a Dayyouth (cuckold). I have done my best to warn him and my sisters about the repercussions of such actions, but he says:" mind your business and let Allah judge me!" and he says this in a way that does not reflect his fear of Allah. In addition to all this, my father is a man with very bad temper: he screams and yells a lot and most of the time for very stupid things!
Sometimes he starts yelling at me for no sound reason. And I am the type that hates being transgressed upon. So I explain to him that he is wrong and that he should not yell at me, but he insists on doing it....I am not the only one suffering from this... my mom and my little brother as well as people at work! I remember when I was a kid I used to be ashamed of my father's Jahiliya behaviors. I am now reluctant to have children or even get married while he is alive... I just don't want my children or my wife to meet him or meet my sisters.
Please advise me on what I should do to overcome this fitna.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

You did well by following the correct methodology, and we ask Allah to enable you to be steadfast on it and increase your zeal in doing good deeds.

You have to know that the right of the parents is great. Allah, the Most-High, coupled His right with the right of the parents saying: "And your Lord has decreed that you worship none but Him. And that you be dutiful to your parents. If one of them or both of them attain old age in your life, say not to them a word of disrespect, nor shout at them but address them in terms of honour. (Al-Isra 17:23)

He ordered us to be kind and dutiful to them even if they are non-Muslims. Allah says: "But if they (both) strive with you to make you join in worship with Me others that of which you have no knowledge, then obey them not, but behave with them in the world kindly, and follow the path of him who turns to Me in repentance and in obedience. Then to Me will be your return, and I shall tell you what you used to do. (Luqman 31:15)

So obeying them in kindness is an obligation, but there is no obedience to them in disobeying Allah.

Therefore, our advice is to be kind and dutiful to your father, He is the patient and you are the doctor. You have to do your best to advise him and explain to him the truth in good manner and with soft words. This does not have to be directly from you. It could be by an effective tape, an Imam, a Dayiyah (caller to Islam), or a friend whom he respects. You have to know that your good relations with him, and being kind and patient towards him, has an important effect in bringing him to righteousness and obedience. Allah says: "The good deed and the evil deed cannot be equal. Repel (the evil) with one which is better (i.e. Allah ordered the faithful believers to be patient at the time of anger, and to excuse those who treat them badly), then verily! he, between whom and you there was enmity, (will become) as though he was a close friend. But none is granted it (the above quality) except those who are patient, and none is granted it except the owner of the great portion (of the happiness in the Hereafter i.e. Paradise and in this world of a high moral character). (Fussilat 41: 34-35)

And do not forget to supplicate, as much as possible, Allah to guide your father and your sisters. You have also to advise your sisters and remind them about Allah with admonition and soft words as well.

To conclude, we draw your attention to two matters:

Firstly, it is not permissible for you to be undutiful to your parents by being dissatisfied or bored by them; or to raise your voice at him. It is not an excuse to say that he wronged you or shouted at you.

Secondly, you should not refrain from getting married while he is alive. It is probable that Allah would guide him because of the good manners of your wife or your children, and their good relations with him as well as their respect towards him.

Allah knows best.