Relationship advice needed

I'm a mother of 3 and he's a father of 1. We have been together for 2 years. After 6months he moved in with us. Everything was great but he has a lot of debt from his past. He was to help out but I paid the bills so he can pay his debt. He didn't, and did help out but not with the bills much (I saw maybe $400 a month when our bills TTL $2200). I was feed up and said you need to learn how to run a house hold before we can have life together. And I asked him to move out. He has been living just Him and his son for about a month now. We were still together and saw each other when we could but he is paying his own way. I found out last weekend from a note book he writes in (that he left out and I picked up to make a grocery list, I did not read it all). I read that he loves me but is confused because He remembers how it feels to have Laura in his arms. Who is Laura? I was upset and asked him who she was he said she is just a friend they didn't sleep with her. I said why was she in your arms? He said he went there and cuddled her on the couch an have her back rub cause she is going through a rough time. I asked him when he went there, he lied and told me it was after he moved out. But I talked to her and she said he didn't sleep with her she has a boyfriend but that she was uncomfortable because she thinks he wanted to. She told me they have been friends for years but that she hadn't seen him since my relationship with him and she has only ever thought of him as a friend. I asked to read his phone messages and he let me but he has been texting her good morning beautiful and ok morning sexy texts or over a month. She says she never responds because she loves her boyfriend and I saw that in his phone, but why is he sending them? Could he be talking to other girls? He said they're friends and she is seeing someone, so if he knows she's not available and he's still with me why is he doing it? Can I ever trust him again? How do you rebuild trust? Can you?

Your right... I know it... But what if him moving out forces him to deal with these problems. What if he can get his stuff together? I love him, don't I owe us the chance to see if he can? What am I to do, I love him more than I have loved anyone before (even my ex husband). If I don't try could I look back a wonder what if...? My question is how do I try? How do you start to rebuild trust?