He didn't cheat but...

Okay so this is long and I apologize in advance. My BF and I have been together for a year and half and have an almost 6mo baby girl. So if you did the math, I got pregnant after only dating for 4 months. We met through mutual friends and they said we were great for each other. The only problem is my BF had a bit if a drinking problem in the past but I was told he has been working on it and for the most part he was. Fast forward to a month after the baby was born. We were on our way to a family BBQ at my moms place and he decided that was the best time to tell me that when I thought he was out of town for work (I was at my moms because I had a horrible delivery and recovery), he actually came home a day before he said he did and went to the strip club and got 2 lap dances - by himself. Obviously I was upset but he assured me it was a one time thing and he was going to go to AA because he was drunk and made a mistake. The next weekend I was using his phone (we use each others phones because hey nothing to hide - usually) and I went to type something in the search bar and a dating website popped up. And can I just mention it was specifically one for "MILF's". I first asked him if he was still in love with me and wanted to be with me and he said yes. Swore up and down that hes not with me just because of the baby. So I brought up the site and he said he was on it because they had sent him an email because he was on the site before we started dating and he went on to deactive it. So I went on to check and yes it was deactivated. I let it go but then the next week he said something about it and how he got it by accidentally clicking a ad. Well that's not what he said before so curious I went through his phone history. Nothing was there. I mean nothing so he obviously deletes it. Suspicious. Luckily I know how to recover deleted history and I did just that. Found out he actually went on the site, signed up, looked at a girls profile and the. logged off. This was a Friday night at 11 pm I WAS HOME. Sunday, again while I was home, he went on to deactivate it. So now he's telling me he doesn't remember making an account but saw an email for one and felt horrible so he deleted it. We have been in couples counseling but I dont know what to do. He had been going to AA but then stopped going and lied to me about going still. He started going to one on one addictions counsleing and I know he goes because the counseler tells me. He recently got a new phone and I went on his old phone to look for stuff for our baby and could see he's been using it to watch porn basically any time I leave the house without him. He swears hes attracted to me but I dont believe him and I don't fully trust him. He has never physically cheated but I still am so hurt about everything. Any advice? And sorry for the wall of text but it wouldn't let me make paragraphs. Maybe because I'm on my cell I'm not sure.