Can this marriage be saved after affairs and False R?

I've tried writing my story here for the past year and every time I erase it. So here is my first post. I'm so messed up in the head and so confused that I need some serious help, advise, reassurance, motivation and honest feedback. Extremely long story short… Myself (31) and my Husband (30) are both have been together for 5 years and married for 3. We have a 4 year old together and he has a 10 year old from a previous relationship that we get every weekend, summers and holidays. Throughout our whole relationship, it seems as if I was "pressuring" him to do right. We have separated numerous times due to his EA's and finding texts/conversations to other women in his phone. I would "kick him out" and few weeks later he is back in the house and we are trying to work it out. New Years was D-Day 1. Found it in his phone. If you go looking for something you will always find it…isn't that what the saying is. Been nothing but the truth with me! He left his phone in the car and it took my hardest not to look but I did and saw that he was talking to another woman since July. He said the affair ended in Sept and that we were going through a rough patch that he didn't know what to do. But it's January and these messages are still in your phone. Last one was in Sept. Sloppy on his part. At this time we were living at his mother's house. I left got my own apartment with my son. No contact for the first week, no apology, no remorse, nothing. Then here comes the apologies, the begging, the I miss you and want my family back and let's date again and start over. A month later I'm at my uncle's funeral and just got all these feelings about missing my husband and wanting our family that I called him that evening to come home. After he came back home we decided to work on our marriage however looking at him and trying to put my guards down was the hardest part for me. I really did try but I couldn't. I told him that it will take some time. We are in this for the long haul but right now I'm still hurt. Even though he was trying his best I was still bitter, cold, hurt and too devastated to let him in. I didn't want him touching me, kissing me no sort of emotional or physical connection. I can tell that he was trying to change and do right but I just wasn't there. My thing was I didn't want him off the hook so easily so we became so distant. Last Thursday June 20th D-Day 2. It's been 4 months since my husband has been back. The moment he came back he promised to be patient and understood why I should still be mad at him and why I felt the way I did. He said he will continue to love me and do whatever it takes to work on us and our marriage. I found in his phone… again… that he was still having an affair with the same woman, the week before they meet up and had sex. I kicked him out again and all he had to say was "I would rather be alone than to be with a wife who gives me the cold shoulder." He said he tried and tried and was tired of me shutting him out. No remorse, no apology, he's out the door leaving to his mom's. Last night after close to a week we finally spoke. I initiated the contact. Aired out everything since the very first time we met. Who we talked to, how we felt etc. everything was out on the table. He said the other woman is nothing serious, just someone to boost his head and have sex with, nothing serious. He said he needed to feel loved and wanted. We talked for hours. It was kind of refreshing getting everything out in the open. Next thing you know we are at our home having sex. So didn't see this coming. This was our first time in 2 months having sex. We had a great night that seemed as if I was doing something wrong. I'm so confused I don't know what to do and how to work on my marriage. If he gets his own place and continue talking to the other woman what benefit does he have coming back home to his wife and family?? It seems like a no brainer but I'm not sure what he wants. If I take him back, once again so soon who knows how soon this will happen again. The table has turned and now I feel I am the one fighting for the marriage again like always. There has not been a point where both of us has put in 100% at the same time! I own up to my part of if I took him back in I should have tried harder to meet his emotional and physical need. I was just too hurt to do and really thought we had TIME to work on us. 4 months back after saying everything I want to hear about working on us we are back at square one. He did say he is not ready to divorce but maybe some time apart to figure things out. Him and my step son are supposed to come over for dinner tonight. I told him my house is an open door whenever he is ready. Was that bad to say??? What do I do from here? I want my husband, my marriage but I do not want to lose my self-respect in doing so. I don't know if a part of me is feeling so rejected that I just absolutely want him back. I know time heals everything but I want to make the most of this time to work on us, if from a distance or if this looks like something that has no future. Any advice, comments anything I am all ear!! Thanks for reading and thank you in advance!

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