Man's perspective here:
I let my wife use my laptop whenever she wants, there is nothing to hide and I wouldn't be furious if she went through the messages, but I would be disappointed if she'd gone back through 18 months of messages to try to find something. That being said, I'm concious that when she was pregnant/just post pregnant, her senses would have been heightened. Doesn't sound like your DH complained about you looking through his laptop, so maybe he did too.
If she ever went through my laptop, she'd have found tens, if not hundreds of messages to other women. That's because I'm a travel agent and 80% of my clients are women - women tend to be the people who book holidays in my experience. Very occasionally, I would get a message from someone who I'd given my number to in a pub/on a night out. I would often small talk before identifying whether someone was really interested in a holiday, and I'd have shut it down if it looked like it was anything else (unfortunately, just like women, men who are willing to chat do get inappropriate messages from women quite regularly).
Some of my friends would cheat, most, including my close friends, don't (this goes for my women friends as well as men). On a stag do, there's likely to be a bit more bravado which might lead to questionable behaviour but at the same time as someone going on a stag do, you are unlikely to know everyone, so it's extremely unfair to tar everyone on that do with the same brush. Unless the stag do's I've been on are very different, most involve too much alcohol, superficial conversation and certainly it would be beyond the bounds of most men in normal life, let alone a stag do, to have a "cheating ring" where everyone else messaged a different woman to hook up with there friends. That's just not realistic and how men generally act.
I don't think OP, your partner did much wrong. It was morally inappropriate for him to set up a mate with a partner, but I'd put it down to the stag do affecting his mind a little, similarly to how I wouldn't judge going through someone's laptop on the basis you've just had fertility treatment/a baby. Taking pictures on a stag do is normal, particularly if a friend is doing something daft. I certainly don't think it's close to justifying him 'not being the man you thought he was' after 12 years and 3 kids. From the thread it sounds on the whole like a decent guy and I would not overly judge him for it.