Finding a Way Back

My husband and I have been together for almost 13 years, married for almost 10. We've been through a lot. He cheated 9 years ago but we overcame. Recently within the last year we've been having trouble. Life is hard with 2 kids, jobs, a house, and him going back to school. He wasn't attentive to me like he used to be. I kept begging for more and more and nothing. We decided to separate but still live together. I ended up being with another guy and realized I didn't want that. I realized the only person I want love and affection from was my husband. I told him the truth and he's trying to cope with the info. I want him and I'm trying to give him space to cope. I just want hope. I want us to find our way back together. I know I made a mistake but it showed me that I was wrong. He's all I want after all. I just want the effort. How can we do this?