Why your husband cheat on you( spy your husband phone)

I was married young, 23, and have been married 10 years. 3 years ago, I cheated on my husband. Why? I needed a listener and someone to talk to. My husband found out, the affair stopped. My husband chose to forgive me (not forget) and stay in the marriage. We have 2 kids.
After the affair, I explained to him what drove me to do it, and he admitted to being at some fault. He changed his ways, listened to me and was there for me. During the last year, he’s gone back to his old ways. Distant, un-nurturing, and doesn’t listen. There has always been a communication problem between us, as we can go weeks without talking to each other.
A few months ago, I noticed a phone number on the cell phone bill at numerous times during the days and nights. I asked him who it was, and he said it was a girl at work (who he knows I didn’t care for). I asked him why he was talking to her and he said at first that it was work related, but then said that he was just being her friend, she needed someone to talk to. I didn’t believe him and told him to stop. No more calls appeared after that, but his best friend who also works with him, called me and told me he did sleep with her, that my husband told him himself. I confronted my husband with this information, and he swore on his kids, numerous times that he didn’t.
He got a new e-mail account, and I was able to get his password, so yesterday I went into it, and saw an exchange of e-mails between him and his ex-girlfriend of 8 years, 14 years ago. Why? So I confronted him, and he said, that his mother saw her and gave her his info. I was very upset about this. Again, he said nothing is going on. Well this morning, I went in to check his e-mail and he changed the password. I called to confront him and he said, “Oh, I felt like changing it.”
So my question to you is, is he cheating? Should I trust him? I want to go to a marriage counselor but he won’t have it, stating, they will not help him or us. My final question is, is my marriage over? My kids are going to visit my parents for 2 months so we’ll be alone for that time frame. Then I’m going to go join the kids and leave my husband at home alone. Should I install spy cam’s in my house? Again, I guess it all comes down to should I trust him?