I have been in almost the same place and first of all I'm sorry for what you're going through! It is hell! I dont want any judgments from others here, this was all my choice and OP wants to know from people who have been in similar situations!
When it happened to me, I found the texts. I didnt read them all I chucked his phone across the room. I was so angry that he could have done this to me, I had given birth to his child! At first I wanted him to suffer. I wanted to break things, end everything and get even. We had a child together, she was about 2 at the time and he said similar things, that our sex life wasnt what it was and that was true but it didnt feel fair.
I felt like I could never get over it at first. The first couple months were the hardest. I couldn't think about anything else. I thought I could never trust him again, I felt sick thinking about it, I was betrayed and hurt, I came close to ending things many times. But as time went on I thought about it more and it wasnt physical and he did show genuine remorse even if he didnt tell me like yours has. He is a great daddy and I believed he still loved me. We talked about what he had done over and over. We talked and talked about our sex life and how it made him feel, I was angry with him but I could see that it had really affected him. He tried to talk to me about it before though so maybe that's why I was able to accept that I had some part to play in it. If he never tried to talk to you about it then how were you to know? Did he ever try?
It was about 3 or 4 months afterwards and I just started to feel a bit better about things. I missed him during this time and I missed being a family. I gave him another chance and we took things slowly. He was very patient and it was sometimes sweet because I knew he was trying really hard and over time he made me feel close to what I did before. It took a long time to get any intimacy back, but when we did it was like a snowball affect and it was like being together for the first time all over again once I let go of it. It was possible for me and I never thought that it was. I always thought I was someone who would just cut and run. Having a break was essential you should do that but set rules for him and yourself. It helped because there was still plenty of pain I wanted to cause him and lashing out at him but now I am glad that I didnt. It also helped me realise that even though this was all his fault, losing him was now my choice as unfair as that was. Having a break made me reflect on what I would lose. You need to breathe and heal yourself.
It's been 3 years and I love him and we are happy. It took a while, but I was glad to be a family again and I was able to put the past behind me. I think about it every now and then, but I'm not angry or sad when I do anymore. For us it helped to bring us closer and I know I made the right choice.
Everyone is different though. You should take time, look after yourself and spend time with your family and friends. You have been together for 8 years and have a child, it sounds like he is remorseful and sorry. No one is perfect and everyone is capable of doing bad things. Before it happened to me I would have been telling you to run away and dont look back, but now I think your relationship doesnt sound like a lost cause. Gather your information and then take that away. Gather yourself and look after yourself. I lost alot of weight during this and I was all over the place to begin with, it's important you look after yourself. Do you have people supporting you?
Hang in there, dont rush anything and look after yourself. If he says he will wait and you believe him, then make him. It's the least he deserves right now. Bring yourself calm before you end things completely. It sounds like you want to have him back, if you do you need time, calm and you have to be willing to make some changes.
I feel for you, it's such a terrible thing to go through but it gets better! Hope this helps