Dealing With Apostate Father and Mother Who Doesn’t Pray

My father and mother have been married for 20 years. In the year 2001 my father went to Agadir in Morroco for some type of affair concerning some type of a restaurant (I can’t recall the exact affair because I was 12 years of age at that time). Anyways, my father committed zina (adultery) and my mother caught him with this sin which he committed on his return home; she did not divorce him due to my young age and my younger brother and sister who were at that time 9 years old and 5 years old.We needed a father so she did this for her children, but she refused to sleep with him for a full year due to the pain she was suffering.
Please note that neither my father nor mother pray, but my mother is on her way to perform salah inshAllah due to the Muslim friends she has. As for my father, when he drinks alcohol, he used to speak badly about Allah and Muhammed s.a.w. in the most horrific of terms which I refuse to write here. The issue is sheikh, now that I am 20 years of age, my father again committed zina in 2008; I was 19 then and did not make salah. After that calamity, I came to Islam alhamdulillah and sought His help and aid. My mother kicked him out this time but now, a year later he is back in our home. My mother uses an excuse like me now being engaged and soon getting married to bring him back, because she can’t spend her life alone without a husband, because eventually my sister and brother will also get married, and she refuses to marry any other good man out there, so she chooses this garbage which I call him.
Me, now being Muslim and knowing the punishment for this sin when one is married has motivated me in doing some actions. I have spat in the face of the woman my father had sex with; she is Russian. I called her by the worst of names in front of all the people, I have almost engaged in a physical fight with my father due to his action, I have threatened him and his lover, and as for my mother, I have raised my voice sometimes when I speak to her on this subject due to her strange choice of bringing this man back to her life after he has done this act once in 2001, and she forgave him, and now again in 2008. I think my mother is desperate, and I want my father out of the house. I have even considered kicking all his belongings out from our door.
Is my actions haram (impermissible); how can I handle this situation, and how should I treat my mother and how should I act towards my father? Should I treat him with respect after this act of his which he has not yet repented from because, first of all he is a kaffir who does not believe in Muhammad.