Great job, T. You sound strong and like you've developed boundaries that you believe in. I'm so happy to see that!
Regarding OW's klassy t-shirt: Well, we knew she wouldn't be of exceptional character if she was messing around with a married father of three, one of whom was a newborn. And to put a picture of them together before word is even out about your separation? Wow. I wonder if that's supposed to pee on her territory or nudge H along to separate from you by putting pressure on him? Either way, it's so wonderful to see such true love demonstrated on social media. /s
H needs to affair down to get his ego fed, and boy is he ever. I know it hurts, but I hope seeing that helped confirm that H is not doing this because OW has something over you. This is, and always was, about H looking outside of himself for something he should be finding inside of himself. It's not you.
Your friend's actions were fantastic, I think. I love that she caught H off guard. What that represented is not shielding H from the consequences of his actions, and that's a good thing. Having it pointed out to him that outsiders find his actions abhorrent is a good thing.
I don't think you need to broadcast what happened, but I also don't think you need to protect him. If folks ask you questions, you can say a vague "Well, the attitude shift started when I was 8 months pregnant. I gave birth not knowing if he planned on sticking around. It was a difficult time for me." I wouldn't tell people you barely know, but for those whom you have a relationship, the above is all you'd need to say. Those sentences plus the picture are enough for them to fill in the blanks about what happened here, and it gives them an accurate timeline so any H blabber about "she went to NC without telling me so I'm done now" looks like the BS that it is.
And for texts, I'm happy you're not really responding. I experienced a great deal of "communication masquerading as needed parenting conversations" with H, who had a clingy, controlling, over-communicative ex-wife. I had to help him sort out what merited a response, and I think I can similarly help you.
The person who wants to use parenting as a way to cling onto a feeling of control of an ex can make any message sound like it's "about the kids." But if you analyze it, it's often them expecting a perk of the past relationship to continue, or it's about their feelings, anxieties, and curiosities. Those things are about the parent, not the kids.
H asking for pictures, or what the kids are doing are not required parenting topics. Those are him trying to act like you are still H and W parenting these kids together. Once you split, your vacation with the kids is YOUR vacation with the kids. You are an equal parent to H, and what you choose to do and not do with the kids is trustworthy.
I've honestly found only two of his messages worthy of a response. First, he asked if you guys made it okay. This is tenuous, because it could be assumed you'd contact him if that weren't the case. But still, "Yes, kids did great. We're here safely." is all that is needed.
The other thing that I think was actually about parenting is him asking to talk to the kids. Good for you for turning that over to the kids. It's not your job to be an intermediary in his relationship with them, (though you may need to assist with things like your youngest holding the phone when he's somewhat capable.)
Everything else has been about H and his feelings, and that's not parenting communication. He's curious - so what? He shouldn't have left or he'd be on the trip with you and wouldn't be curious. Or he'd take the kids on their own trip. Honestly, you do not have to tell him what you're doing with the kids. It is your time with them, and after a M ends, such inquiry is intrusive and unnecessary. You could just ignore those, or send a "kids will share with you next time you see them" to set a boundary.
Asking for a picture is similarly a perk he used to enjoy as your H. His inquiry is intrusive, and if he wanted to feel involved, he should not have left the marriage. Not having moments like those is one of the downsides of D.
It's up to you what you want to do. Maybe you want to send pics because you'd want him to do the same, for example. But it can be difficult to sort out what is about parenting and what is an intrusive remnant of a relationship that has ended when you're still spinning from the relationship ending.
Honestly, anything can be creatively made to appear to be about the kids. "I forgot to buy macaroni at the store for kid. I can't believe you didn't remind me!" is one. "It's your fault that kid2 picked his nose at the assembly. You were such a bad father" is another. "Word got out to the neighbors that kid3 broke that fence. I'm so mortified and I have a lot of feelings about it." and "You can't bring your new BF to come pick up the kids." are others. All of these look like they're parenting because the mention kids, but all of them are about the feelings of the person typing them, or an attempt to keep up arguments that are a remnant of the M that has since ended.
Do you see the difference? The above are all unnecessary communication that have been "made about the kids" through a little effort. If it's not directly about: physical or emotional health, schooling, extracurriculars, finances, or discussions about vacations/parenting time requests, then it's not about the kids and you are free to totally ignore it.
I hope that helps. I see that you've grasped onto some freedom that you aren't beholden to H and what he wants from you in texting, but I think there's still more freedom there if you want it. It can be a confusing time and so I hope I helped you see that the majority of the stuff H is texting is about him and his wants and needs, and those are now irrelevant to you.