How to break the cycle?

I'm pretty stubborn and sometimes I like to think that I can completely cut my ex off and move forward completely all by myself, but I must admit it's not easy. I'm so used to going back to him or speaking to him even after he's wronged me that it seems like the norm. I'm embarrassed and ashamed that it's so hard for me to completely let go, I've come to a point that I really want to let go though. I've posted on here numerous times and all those times I've received amazing advice and responses telling me that I have to let this go for my kids sake. Then I find myself back in the same cycle a few days or weeks later. Then once I'm communicating with him again and he's back into my life I'm completely miserable and ask myself why I allow myself to be treated this way. He's the only person I've ever been with, I've been with him since I was 18 so I fear moving forward. Since I've given birth nothing has change as usual. He ended up losing his job which wasn't really he fault it was because he had to keep missing work for things he needed to do with school so I didn't judge him for that. After that, he ended up leaving his pharmacy technician courses because he kept failing the classes. I tried to be there and be supportive towards him because he's experiencing a hard time because he's also homeless but as usual he began to take my kindness as a weakness. He would ask me for money and if I failed to give it to him in time or if it would take long he would become very disrespectful and call me names and threaten to stop speaking to me. If he became really upset he would use the kids as a weapon telling me he would take them away from me. After a while that became the norm. He would text me telling me he had a lawyer and expect to lose my kids I'm the upcoming months. He would tell
Me that he tried to do things the right way and allow us to be a family but I was compliant to his needs. I told him that I didn't think we should be together because the relationship was unhealthy and I didn't want my kids to grow up with two parents that were constantly off and on and always arguing. When I would say this he would get upset and tell me that I wasn't a good mother because I wasn't trying to be with him and we only argued and he only broke up with me because I didn't do the things he needed done. Which are getting him a place to live and making sure he's okay. Then he told me that if I cared about him at all I would put the down payment do he could get a place to live. He told all his friends that I was horrible to him and left him out on the streets instead of helping him but why would I bend backwards to help someone that's constantly hurting me and leaving me for other women? The stress of taking care of two kids and a newborn alone started to overwhelm so so I asked him if he could take the kids sometimes for a few hours so I could get things done and he could spend time with them. He would tell me that he was broke so he couldn't travel and would only be able to come help if I sent him money to come. After a while I broke down and sent him money and of course he didn't show up to help me and even yelled at me for sending such little money. He kept on telling me that he wanted us to be together and to be a family but yet he would be on Facebook sending naked pictures of himself to other women meanwhile telling them sexually explicit things. I will never understand why he plays games like he does. It's like he only tells me he wants me so I can do what he wants me to do. I ended up moving to a new place and was weary of giving him my address because when he's upset he threatens to hurt or kill me. He used that as the reason why he didn't want come see the kids. So finally I gave him my address and of course he still didn't show up. He makes plans to come and see them and then he calls and says he's coming but never shows up and doesn't even call to cancel. He doesn't have a phone anymore which I understand but he makes no attempts whatsoever to call his kids or check up on them to see if they're dead or alive. I see him
On Facebook talking to his friends and having time to make plans for the weekend but it's like his kids aren't event important enough to send a message seeing of they're okay especially knowing his has a newborn. I don't understand how he can go days and days without even knows if they're okay or not. It's like he acts like a father when he feels like acting like a father. I want my kids to have their dad and I hate women that cut their kids fathers out the kids lives due to their own selfish feelings but I don't feel like he acts like a dad and I've given him so many chances. Even after he's disrespected my kids and called them names when referring to them telling me he doesn't care about them anymore because according to him he's cared too much. Is it wrong for me to just cut him off completely?