Is it me that's the problem?

Fuck me, he acted like a dick!
If he's not a full-blown dickhead all the time, then I'd sit down with him when both calm (maybe after the kids are asleep) and list all the things that need doing in the evening/morning to prep the kids for school. Then you split evenly who does what.
E.g.:

• prep DC1 bag for school? Evening, DC1 + Dad
• help DC2 and DC3 with breekie? Morning, Mum
• packed lunch for 3 DCs? Morning, Dad

If he is a full time dick head...

Your DH shouldn’t have shouted but having to help a teenager find a booklet is ridiculous.

Older kids need to get into the habit of getting themselves organised the night before.

If the younger child refuses to eat breakfast in time, well, she goes hungry. She’ll learn.

I agree with @NotbloodyGivingupYet , you're pandering and running about like a skivvy to your kids.
Do they do anything for themselves? You're full
of excuses, the comment about blaming your DH for the wee one being tired is petty.
You've made yourself the centre of this, they need you to sleep, they need you to find things etc etc teach them to do things for themselves or you'll be packing their bags at 18 as they'll be inept.

He doesn't want to "help" so he is doing what he is doing so that you get fed up of asking him.

But your teen should not be rude to her father even if he is being a prat.

There is no need for it to be so chaotic in the morning.

You all need to have your roles more organised so you don't end up doing everything.

Your husband's way of handling things is shit, but it really didn't need to get there.

Bags and lunches done night before.

Breakfast made available, if it's not eaten, they go hungry and won't make the same mistake again.

It sounds really hectic and stressful, but it's definitely a case of fail to prepare, prepare to fail.

How old are they?

Sounds crap altogether.

Sorry but I disagree. If she is a child who is doing a drama thing or getting up at 5 to swim 50 lengths or riding a horse all weekend, the normal stuff still has to be fitted in and she has to learn that being organised is even more crucial. Putting stuff back where it belongs so it doesn't end up lost is a hugely important life skill and making a lunch box in 5 minutes flat, because she is shattered and wants to go to bed, is not going to kill her. Presumably the only thing she actually needs to create , rather than picking up and dropping in the box, is a sandwich.

All of this.

Your household sounds chaotic and stressful. No wonder everyone is shouting and crying.

Why are they doing homework in the morning if you're in such a rush? It will never get done properly! And why is your husband helping your teen child look for her school books?!

Jesus it's making my blood pressure rise just thinking about this 😂

My ex husband was like this, we have 2 children together 13 and 9 but I left him because he was abusive to my children and me. I am now in happy relationship with my new partner and we been together for 2years we have just had little boy he's 3weeks old and I couldn't be happier if I was U I would be really think is it worth it? Does he make U happy?

Btw I wouldn't say you're 'the problem'. I was left to my own devices as a kid and remember walking to my friend's house so we could walk to school together, and absolutely marvelling as her mum put cereal and milk and a SPOON together for her daughter, made sure she had everything she needed, etc. No one had put milk in cereal for me for years and I was ten at that point. There was something so caring about it!

My kids have croissants, juice, milk etc for breakfast - we set things out for them on the side the night before so they can get their breakfast in the morning. I think encouraging independence is good, there's a good balance to be had in caring and nurturing your kids enough that they have the skills to grab some brekkie in the morning. I do get your perspective as I am often led by my heart to do the same, especially after my childhood! But there is a happy medium. It is not spoon-feeding your kids, and it isn't shouting and removing pocket money and weekend plans over a missing book or whatever.

I think it might be a bit late now but it’s madness to fall into the habit of doing absolutely everything for your children. That is not helping them at all. I was brought up to pitch in practically from being a toddler so I brought my children up the same way. We all help, we all do things. Yes, I do the most as I am mum and I run the house but I don’t do everything. Breakfast was always self-serve. PE kits and stuff for school was on them. I reminded them but I didn’t do it for them. Actions have consequences. They need to learn.

Understand your frustration with your DH. My ex was the same. Useless. Wanted to be told to do every little thing. No initiative and no patience. I had him leave when my youngest was 10. He was just another child to take care of.

Just saw your update.
Your DD would have been better off sorting her stuff out the night before. It was a false kindness getting her to leave it until the morning. It's really hard to try and get yourself up AND organised when you're really tired after a long day and late night.

Doormat meets short fuse

My 11 year old makes sure she has the right books in her bag and both children (9, 11) get their breakfast in the morning.
How old is your youngest?

All of this. You need to do as above and have a meeting with your husband. Then you need to have a meeting with your children about what is expected. School bags, PE bags , cookery stuff, specific one off stuff like book day, Easter hats ( whatever bollocks school have thrown at you ) is absolutely, and with no negotiation, to be sorted and put in the hall the night before. Breakfast is freely available. They can get it themselves if teens. If they don't eat within the available time then they go hungry. That's on them. No one died from lack of toast .
NEVER EVER EVER UNDERMINE EACH OTHER IN FRONT IF YOUR CHILDREN. You asked him to do something. He did it in his way. If he shouted at them then tough on them. Some people are Mary Poppins some people get pissed off when people,who could help themselves, are not doing so . If they don't like being shouted at they coukd avoid that by doing their jobs so the house runs smoothly.

To be fair I think OP’s point was she wasn’t letting the youngest walk away from the table without eating but because she was on one person she needed the DH to do the “not letting”, ie go and get her. Once she’d gone this was the only way of “not letting” - shouting and screaming up the stairs in the mornings when everyone is tired isn’t helpful.

If she’s 12 she’s not a teen! Just read this drip feed.

Sounds like the book was easily found so the point still stands - my 16 yo is also incredibly hard working so I get it but they need to know that extras are extras, not instead of the basics.

You are mollycoddling your kids. They ought to be more than capable of sorting their own school bags, doing their own water bottles and PE kit. Ans as for wandering off and crying instead of eating - not even my cat does that! And you offering alternatives is ridiculous. If she refuses to eat, fine she gets nothing.
Be firmer OP. Set aside 15/20 mins in the evening to get it all done. This all sounds pathetic and a chaotic way to start a day.

He is very unreasonable. He’s deliberately being worse than useless so that he isn’t asked to help again -now that the ploy of needing to giving specific tasks isn’t working he’s trying something else.

I do agree that it would help if the kids were a bit more self sufficient though, esp the teen.

Then perhaps she's doing too much?

It sounds like chaos.
You are running around pandering to your children and training then how NOT to be independent.
He is trying to keep out of it beyond practical stuff like filling water bottles and toasting a bagel.
Frankly I'm on team DH (apart from the shouting, that's bad).
Why are you letting your youngest walk away from the table without eating breakfast, then expecting someone to personally escort her back down?
Homework and bags should be sorted the night before. Lunches should be prepped the night before, so morning should just be putting bits in lunchbags.
DC should be doing much more from themselves. Put cereal and milk on the table, they can serve themselves. Bread next to the toaster. Fruit bowl on the table.
If you want your DH to help, then agree between you a better morning routine, and let him help in a way that makes sense. Sending him off to "help" children who should be helping themselves is a waste of everyone's time, and given his short fuse in the mornings, doomed to failure.

Mornings are stressful with three kids and instead of pulling together you’re turning on each other.

Sit down and tell him that. Tell him you don’t want to be the kind of couple that bickers over kids and you want everyone in the family to have a good start to the day. Come up with a plan together, a list of things that need doing in the morning and who is responsible for each.

Why not just talk and plan out who does what in advance, also your teen could be doing a lot more for themselves.