how to break up with and kick out abusive narc bf? F20 M22

we're 20F & 22M and we have a one year old together. we recently moved into my mothers home because she fell ill with cancer and requires a caretaker ( me ). this has made leaving more difficult. before, my plan was to just break up and move into my mothers home.

we started our friends. our relationship was really great. i whole heartedly believed he was the one. i loved everything about him. soon after we officially got together some stuff happened with his family. he became visitation supervisor for his little brother and step mother. she's very abusive ( she abused my bf growing up and his father, her husband ). throughout the visitations that were hosted at our house she would stick the little brother in the house with me and smoke weed outside the whole time with my boyfriend. i resented these visitations because it wasn't right. i knew what the both of them were doing was wrong. every weekend he would yell at me because i objected the visitations. he couldn't see what i saw. ( he does now. we are in NC with her ) this is when the abuse started. yelling at me and screaming at me triggered my ptsd from my abusive father. we've had a talk about his behavior every few months since this began almost 3 years ago. he's aware. after a year of being together we got pregnant. 10 weeks into my pregnancy i found out he was messaging women to hookup while he was out of town working. after i confronted him he trapped me in our bedroom and began destroying stuff. this was the absolute downfall of our relationship. i was scared to be a single mom so i stayed. i started therapy for support and begged him to also. while i was pregnant before we had our daughter we went out one last time so he could shoot pool before she came. i have astigmatism and can not drive at night. he drank even though i begged him not too. my cars passenger seats airbag signal is on and so it's the seatbelt. the cars previous owner had problems with it. it wouldn't work. anyways he's speeding home doing almost 85, drunk on curvy back roads. i'm 9 months pregnant and scared to death we will wreck and my baby will die so i ask him to slow down. he yells at me and tells me not to ruin his fucking vibe. i freeze up and just cry well he tells me that pisses him off even more he continued yelling at me up until our daughter was born. 5 months after i told him i forgave him for his cheating, i find naked women in his phone. i packed up and left. we spent some time apart and he told me he's starting therapy and that he will change. that was in july. i carry a lot of resentment towards him. i've lost all trust and respect for him and he knows it. he has no patience with me or our daughter. he tells me blatantly that he doesn't want to deal with her when he gets home. he tells me my standards are too high. he tells me he will never change. i walk on eggshells constantly because you never know what will set him off. everyday is something. last week i was determined and we sat down and i told him i was done that i was ready to break up. he told me he has changed and that im not trying hard enough. his "change" is he hasn't yelled at me in 2 months. he insults me. he sexually coerces me. i didn't know what he would do so i recorded our conversation from that night but he went in my phone and made me delete it. he gaslighted and manipulated me the whole time right back into staying. he said we will do couples counseling. and ps he NEVER started therapy after he said he would. he said he doesn't believe in it and that if he did it it would just be to shut me up. it's a repeating cycle of we have a conversation about his behavior, he says he will try harder, he starts hurting me, then i don't want to put out, that pissed him off even more, then we have another talk. its the same damn cycle. he drains me. i desperately want out i just keep holding on to what i had hoped for us. someone please give me specific advice on how to break up with him and kick him out. he doesn't have anywheres to go ( i know that's not my problem ) he's currently out of town for work.

thank you all in advance. i really need some support here. i am READY to leave.