I don't have young kids but these are my thoughts
When my husband goes out, he sets an expectation of his return time, "will be back by midnight". If that changes, in that he is coming back later, I would expect a text regardless of kids being involved. Given you have a young baby and have been struggling with sleep, I would expect that text to say something along the lines of, "having a good time and planning on going back to mums for a few drinks if you don't mind, any problems text me and I'll come back!" So if I'm asleep at this point , when I wake up I know where he is and not to be concerned but reassured he has spared some thought with me at home with kids, specifically a young baby. If he subsequently decides to stay at mums, I would expect another text.
I know in this case you are confident of his whereabouts and trust him, the issue is his lack of consideration for your peace of mind.
But... and this is many years ago (1960's), my dad loved the old fashioned dinner dances and with three young kids mum couldn't or didn't want to go all the time. So dad went with his mum, dad, sister and her husband. His mum and dad were landlords and could drink. They used to have photographers in attendance (way before mobile phones). Weeks later the family would produces photos of the family, all dressed up having fun. To cut a long story short, dad met someone at these events and she became a regular fixture at these outings. My grandparents thought it would blow over and was just a blip. Then they decided it was their son and if he was unhappy with mum they had to support him. Mum eventually found out as some kind soul showed some group photos from the event that had been hidden from her previously. It was a nasty divorce, not least because when my mum had an inkling dad was pulling away and discussed it with her SIL and MIL, asking for guidance, they repeatedly told her she was imagining it!
So you are confident in your relationship and thats good but your husband needs to appreciate that he needs to show common decency and tell you if he is not coming home and where he
will be as not everyone would be as trusting as you. Ultimately its about respecting your peace of mind. When he loses that respect and trust, the marriage is done!