I am not going to hound you and I am sorry if this upsets you, so my last contribution. It is very nice if he is cuddly and seems pro-baby and good company when he is beside you. How can you trust him when he is out of sight?
I am not saying you can ring fence him and decide who he is friends with. There is a difference between open friendship and FBing or messaging ex girlfriends. It is too easy for someone who has "'fessed up" to say,
"Oh Sunnydale, you knew what I was like, yet you chose to stand by me".
Perhaps his frankness was attractive, maybe you thought he is not so bad, a good daddy, possibly you thought he was absolutely sincere.
No woman pregnant by a a partner wants to think of him as anything but loving and decent. I sympathise you are keen to stand up for his good qualities rather than "Give a dog a bad name and hang him".
When I confronted him about the messages he was calm as I had the proof so he couldn't deny it.
I should think he was "calm", how could he deny it, were you calm? Did he apologise, make promises, toe the line?
However, does he now feel he got away with the messages so I don't really mean what I said?
I'm afraid so.
He may twist any doubts and he may say he regrets being honest and upfront, if now you are suspicious and don't trust him.
It is good to start afresh, no secrets, but you can't ignore what your instinct is warning you. Telling you about how shabbily he conducted his last relationship isn't proof that he will now be loyal and faithful. It's not even restricted to out-of-town ex gf is it. He didn't stray far when he had an affair with a colleague did he. That was past history but I hope it's not present.
If he is turning down sex with you and has been sending sneaky texts at least since last summer, does that seem normal? How will he be when you are 7 months' gone? Occupied with newborn twins?
Tbh I think if you go down the road of, It must be my fault, not keeping him happy, poor him he will grab that excuse and flout that. Good luck.