Saying please don’t drop daughter caused resulted in silent treated

If DH was dicking about - or regularly does dick about - with her in a way that put her at risk then telling him to be careful was warranted.
If it was intrusive thoughts then it's understandable, albeit annoying for him.
However if you're regularly telling him what to do when he's already being diligent then I understand why he was pissed off (though not enough to sulk all day).
Saying my child was insensitive.

Sounds like there's wider issues at play and you both need to act like adults and talk. Regardless of what you said was justified or not, it's ridiculous for any adult to sulk all day as a result - especially on holiday.

Bizarre voting imo. Some kind of worldwide humour outage maybe.

Does he have any reason to suspect she might not actually be his daughter after all?

Unless your DH has form for dangling toddlers off very high historic monuments, then yes, it was a twattish thing to say to a competent adult parent.

Sulking is childish, but if you often 'joke' in this fashion, I can see his point: I wouldn't want to spend time making conversation with somebody who treated me like an idiot.

A joke is only a joke when both sides find it funny.

I think your comment was crass.

Did you apologise for it?

If he continued with the silence after your apology, then he was also BU

Me and my dp do this too. Or if one of us is popping out somewhere we often say watch your child/children am going to abc

Id find it annoying if someone said that to me.

Do you have form for digs and patronising? If so then his response is understandable.

I think your DH needs to chill, it was a joke right? I joke around with my DH all the time about our girls when they do something. I say "well she's your daughter" its only a joke ??

will this marriage last, do you think.
seems like a lack of respect in the mix.

Perhaps he feels undermined by your comments. Do you often say things that mean you are the parent with the experience/knowledge ?

Exactly this.

Oh goodness me, I thought I was easily offended. Clearly not.

OP, is there a back story/more context here? His reaction seems disproportionate and a tad abusive.

I will jokingly and sarcastically refer to our DC as “my Precious First Born” if I’m being the overbearing one and he’s doing something silly with her. So I think there’s not much wrong with your comment tbh but clearly I’m in the minority here. My DH would not have batted an eyelid as he’s secure in how equally effective he is at parenting as me. Your DH sounds insecure and childish. If my DH was upset, he would have calmly and politely said “She’s my daughter too. She’s safe with me.” but silent treatment is not a thing in our marriage. It’s unnecessary, not how adults do relationships, can be cruel and, like I said, can be abusive.

Don’t be told/made to think rather his silent treatment is a reasonable response.

It's the sort of thing my DP and I would say as a joke. Like when they do something naughty he might say "your son has just done xyz"...it's kind of said in a tongue in cheek way. We also shift ownership of the cat from time to time...I think your dh over reacted.

I think this is probably a symptom of a wider problem. To you it was a light hearted comment, to him was it one of many digs? Do you have form for treating him like an inferior parent? Being possessive over dd? Treating him like he doesn't care as much about your dd as you do?

It sounds like a straw that broke the camels back situation and you need to talk to each other to get to the root of it.

I can see how he might have felt quite embarrassed by the phrasing ('my') of your request seeing as you were in public.

Both unreasonable but I can see his is in response to you. Why did you feel the need, even lightheartedly, to say about dropping the child? Secondly, why did you call her your daughter? Both very odd things to say...

I can't bear people who sulk and give the silent treatment, so I'm more on your side than DH's. That was an annoying comment though! It may have seemed light hearted to you but I can see how he found it irritating. Have you kissed and made up now?

Unless he’s prone to dropping things or being generally clumsy why on earth would he need a reminder to be careful.

I would have been irritated too not sure I would have sulked all day though so I’m wondering if a) he is prone to sulking or b) you are prone to treating him like an idiot?

It’s allowed to say my child. It’s not that deep.

I don’t see a problem with reminding him to be safe but calling her “your” child is very telling. Imagine of your DH referred to your kid in that way as “his”

He felt the need to punish you for the whole day just because you felt anxious about the baby?!
I don't like the sound of him at all 😐

If it was a one off and lighthearted then he’s the twat. If it was the latest in a long list of micromanaging then you are.

Saying "my" daughter to her father is a really odd thing to say, sounds so passive aggressive.

What did you think he would say "Awww shit, I was just going to drop her actually, but you talked me round", calling her "my child" is also quite an arsehole move.

Did you apologise when you realise he was pissed off? I would have probably been quite quiet for the day too without an apology.

If he sulks regularly then that's a different issue, but if this is a one off then I think it's on you tbh.