I'm really sorry op that you've been given such a hard time on this thread, clearly there are many posters that have no idea how emotional abuse works within a relationship, or how emotional abuse can be different between the two sexes.
You are right, he was being very disrespectful to glare at another woman, especially as you were 'trying' as a family. I also can fully understand how you wish this relationship to work, he is the father of your child. This was a test, a test that he failed, all he had to do was be fully present and in the moment with you whilst on a day out.
It's not that he couldn't do it, he choose not to do it, now you have to question why, do you think he did it on purpose, because I do.
It's a form of triangulation, even with strangers, it is done to make you feel insecure and neglected. It has worked and it will do forever more.
It is also used to make sure you don't request family days out anymore as they become too painful for you, he is then able to do what he wants with his time and further neglect you.
Other pp's are correct in saying that any upset or silent treatment will go over his head, he won't be bothered. I don't actually think you meant silent treatment, people who dole out that don't post on mumsnet stating they are upset by feeling neglected and disrespected.
Op you would be far better off researching about abuse, looking up about narcisists, it would give you an idea on why he does that and his motives. I really don't think he will change, he will be insensitive, arrogant, selfish, untrustworthy and many more things forever more.
You will not change him, you gave him another chance, drop the rope, stop trying to make him 'nice', he likes it this way and he will not stop being the one who feels the best and takes the best out of your relationship.
He will suck the very soul out of you, gaslight you and make others apear you are the one in the wrong, just look at this thread. When you are in an abusive relationship your whole identity suffers because they have you analysing the small stuff all the time, it will send you crazy.
Look at the bigger picture and see this man is no good for you he is stealing your spirit.
I can see that.
Now op's back off, this woman is being damaged as we speak.