Please really need Advice!!

Monica • One happy mamma! 😍 💙👶🏼
sorry so long but could really use some advice... btw I took my engagement ring off cause I'm not going to be engaged (again) with this going on. 
 Me and my fiancé has been together going on 3 years and we have a 1 year old child. Iv noticed he has been acting weird lately so yesterday I looked on his cell phone and he has been texting a girl from work. He told her she's beautiful 3 different times, one being when we were home drinking and he told her he was with friends. He only brought me up twice and they been talking since February 1st. He text her every morning "good morning ". He barely text me ever. He has made him self sound like the worlds greatest dad in the text. Telling her " took my boy to the park then grocery shopping got him healthy snacks" I was there but never brought up. 
 When we would be together watching tv at night, we would be talking and his phone would go off. He would drop me to answer his phone. Been telling me it's a guy from work or fb. Come to find out it's her. Has her on fb and Snapchat. And see each other at work every day. 
Right after I seen the messages I was so pissed. This isn't the first time it's happen to me. My ex did the same with a girl from work and now is with her. I was with him for 8 years. 
I told him right away. Read all the messages with him watching. His thing is they are just friends, doesn't even want anything to do with her.. what I can't have friends! Iv never had a guy friend tell me I'm beautiful 3 times and the way he did. Later after thinking much about it I told him I don't think I'm going to get over this. We talk and he apologized said he didn't mean anything by it. He said he wasn't going to text her and try and stay away from her at work. Iv been through this just didn't have a child with that person. He said that he feels he talks to girls like that because he feels not appreciated, and I talk down to him. In the 3 years he has talked and deleted messages from an old friend, found out when I would be at work he would be constantly watching porn, quit his job with out me knowing, got arrested when I was 8 months pregnant. Turns out he stole at that job and got fired and arrested. Now this... do I keep hope? Do I waste more time? What would you do if you were in my position? Also I looked on his phone this morning and she texted him "hey (his nickname) " at 6pm. He never replied.
Me and him talked and he seemed really sincere about his apology so I'm going to try and work it out. But i was thinking about either me or him
contacting her to let her know It's not ok. 
My question is.. should I do it or him? And even if he dose I'm going to be helping him word it. But what should it say to were it doesn't come off in away of her talking about us or me? What should it say ladies?
Should I not even bother.. my worry with that is I don't want to ask him or thinking about if she texted him that day. But if she gets this message and still messages him I'll have a reason to be upset. Please help me out ladies!!