How do I repair things after shouting at my teenager in public?

I think your ds has learnt an important lesson about his own rude behaviour.

Was your younger ds telling the truth about what happened? Personally I’d leave things be for now & let your older ds process what happened.

Would you chance another holiday in the future given how your younger ds has struggled? It must be very tough OP.

Eeek, it's not great. From his side you've ignored him all holiday and stayed with his brother, not listened and minimised his feelings when he told you what was wrong, and then shouted at and deliberating embarrassed him in a shop, again siding with his brother who has totally ruined the holiday.
He's not dealt with it well all week, but you were the adult here. With other adults. You're going to have to apologise and then prove through your actions that he isn't second to his brother all of the time. Whether your younger son is dysregulated or not, your oldest also needs time and energy putting into him.

So he was 3 years when his brother was born.

Sounds like he's had a lifetime of playing second fiddle to him.When you're the only one who can keep your youngest calm. Who kept your eldest calm when he was having problems or did he have to pull himself together because of his younger brother who you always had to prioritise.

He hasn't seen you for the entire holiday because you've spent it all in the hotel room with his brother and you shouted at him and humiliated him in public in defence of your darling youngest again

You have two kids, perhaps you would do well to remember that. You speak as if you have one.

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I sympathise as I have the most provoking 14 yo in the world and I have screamed at her on occasion and felt terrible.

Later when things are calmer you go, you hug him, you say I’m really sorry I spoke to you that way but you must understand your behaviour led to that. I love you very much and I don’t want to shout at you but you cannot disobey and swear at me or I will get very angry.” Also make it very clear you didn’t want to spend so much time with the younger one and try and spend some 1:1 time with him.

Don’t do some grovelling apology that makes it sound like it was all your fault - it wasn’t and he had no business using the f-word. He needs to understand that swearing and provoking behaviour have consequences.

Remember that when we were growing up we would never have spoken to our parents that way in a million years. We’ve been more gentle with our children, but they need to understand there are boundaries.

I might be the minority here but I probably would have done the same. There’s only so much us parents can take. I have a teenage daughter and she is good but it’s the back chat I ignore it but when she does it in front of friends and trying to be smart that angers me. He’s 14 he knows better than to be behaving like that and especially the swearing at you!

Who were the extended family? Or have I misunderstood and it was just you and your 2 children?

I think you need to apologise. I do wonder though whether because of his needs the youngest demands more attention which the eldest is frustrated about. Also knowing this, maybe the youngest told a lie about his brother as he knows you tend to be on his side about things.

So your eldest misses out on holidays because of your youngest.

Your youngest again?It's really all about him, isn't it.

Because he's never the priority. You fit him in when the other child permits it.

Wow, what a dick response.

He learnt the hard way about fuck around and find out. I’d have given him a very public bollocking too

that being said sounds like your youngest has taken up an awful lot of your time this holiday to the exclusion of the eldest and that must be hard for him to see him taking all the attention.

Exactly I wouldn't instantly believe everything the youngest says. Youngest probably knows.Mum will go charging straight to his rescue and she absolutely did

That's the problem. He's sick and tired of the youngest being prioritised all the time and I feel very sorry for him.

It was the other way round when I was a child.I was the youngest, but my sister had mental health among other issues, and everything was about her. I never got a look in. Everything we did had to make things easy for her.And I have to say, the resentment, I have carried long into adulthood.

I get it by the way I’m a lone parent of 3 constantly guilted that I’m not spending enough time with each of them. One also has some pretty serious medical conditions.

personally I wouldn’t have taken them on holiday given how the youngest is as it just makes the difference between the two children stand out and has caused even more resentment. I’d have taken the eldest out for some more 1-2-1 days

Why? It seems quite reasonable to me. Youngest child gets (and probably needs) all the attention but noone is looking out for the oldest. Of course it isn't easy or fair but the oldest needs their needs acknowledged even if it is just saying out loud that this isn't fair.

Are you really this cruel and unable to read ? OP says "right now" to the most basic comprehension this explains how OP is feeling in the moment and is not a firm commitment.

Did you enjoy being unkind though?

I think give yourself a break. Teenagers need to learn that parents are human. It sounds like he deserved it. I doubt anything else would gave got through to him if he'd been like that for the whole holiday. Making fun of his brothers tics is unacceptable.

He's only a child himself even though he's an older child. You can't apply adult logic to it.

He probably felt upset that you were only willing to spend time with him when your youngest didn't need you and said no.

Couldn’t disagree with you more.

Well I can see both sides here completely. He’s 14 so totally self absorbed as all teens rightly are. From his perspective you absolutely do prefer his brother since you give him most of the attention. He will be able to rationalise and understand why but it won’t make it feel any less fair at all. This was supposed to be a family holiday but you spent it locked away with his brother and he was, what, alone by the pool all week? Of course he was miserable and of course he lashed out. He’s clearly crying out for some attention.

Your perspective is you’re a single mum so have no back up to give both kids attention. You had to help your youngest this week and then on top had to deal with oldest being rude, swearing at you etc. He definitely shouldn’t swear at his mother, it’s completely out of order. You snapped after what sounds like a tough week, understandable.

Going forward, do you have relatives who can help with youngest? Respite care at all? Your eldest needs some 1:1 time.