DH won’t pay into children’s savings accounts

This a million times over!

He may have no spare cash. You work part-time and you have two DC and he earns 47k, which is not a great deal these days. You outed that he pays nothing into the children's savings account in front of his parents and you nag him. No wonder he said you embarrassed him and he doesn't want to put money into an account.
You could perhaps have a joint account into which both your salaries go? Then you might see where money is going - I get the feeling you do not know how your DH spends his salary or how much money is 'spare'.

Why don't you have a joint account? You should both be putting 50/50 into the account. Even if it's just £20 a month. Sit him down and tell him if he doesn't add money to their savings then how does he think it will look when you tell them he added nothing.

So he barely has anything leftover - 2k is nothing for a family of four. What will you do if the boiler breaks, or the car fails its' MOT, for example?

Because it's a manipulative and unpleasant way of trying to get him to do something.

If it's no big deal why would it embarrass him?

Many people make this mistake - little children become bigger ones , and once theybaren18;they have total control over an account you put in their name . They might want to spend it on an elaborate tattoo, cosmetic suregery, drugs , gambling , the list goes on - some things you will approve of some you won’t , but perhaps your husband is more aware of this and thinks he will contribute at that time if it’s appropriate and a good use of funds for the whole family.

OP, I think you've been given a bit of an unnecessary hard time, partly because there are several issues here that are causing confusion.

1. Sounds like you have children with someone, and have sacrificed your earning power to do more of the caring for them, but your finances are not properly joint- which makes you and the children vulnerable.
2. Sounds like your DH is bad at managing money- overspending in the past, and even now spending everything he earns every month unnecessarily, and at the cost of your family's security. Meaning that you, on a third of the wages due to being the main child carer also, is carrying all the burden of trying to save.

1. Sounds like you disagree on whether to put money aside explicitly for the kids in the kids name. This last one is what you led with, and is actually by far the least clear.... because saving explicitly in children's names can be a headache, especially if you don't have tons of financial security. It makes it impossible to get the money back, even to pay for crises. It becomes legally theirs at 18, and they may not spend it wisely. And it can distort benefit calculations I think.

I'd say the real problem is the top three issues.

I'm not on the highest pay , in fact currently on maternity but you bet I pay £20 into my daughters bank account without fail , every single month

I’m sorry I see there a disability is the reason why you can’t work. I should also clarify that I think saving if possible is essential in a family, but doing it in your children’s bank accounts is a choice. We save every month but not in our children’s bank accounts. I would rather be able to fund things they need rather than they get access at 18 and blow it all.

Many mums with children work full time, it’s far from clear it’s not possible. It’s not obligatory to save in children’s bank accounts, we don’t, it’s just a parenting choice unlike keeping them clean and fed and reading to them which are all basics of good parenting. Your dh doesn’t want to. Why do you think you get to insist? Can’t you talk like adults?

There is no way on a salary of £47k a month that he has surplus of £2k a month whilst supporting a family of 4

The latest update brings to the fore a more serious issue arising from your separate finances. Whilst he keeps a £2k float, the £2k surplus each month is being spent by him. On what? Is it truly disposable income or are you under estimating the essential bills and expenses?

If he's actually frittering a large amount of disposable income on himself and not sharing it with the family, that is the real problem.

Disclaimer: I've nothing against separate finances if overall the arrangement is fair and workable.

So he’s actually spending everything he earns each month. Which means he’d need to cut back somewhere in order to redirect money to their savings.

your DH does not appear to be dictating what you spend your money on - you have separate finances, if he was telling you what to spend your money on everyone would be saying he was being financially controlling.

I think it is very reasonable for this not to be a priority to him.

I don't have a savings account for my kids. I feel awful.

Stop asking him to put money in their savings. Just keep adding to it yourself

How do you end up married for years, with children, and you can’t come to an agreement on how to manage your (joint) finances and savings? Or whether or not to save for your shared children? It just baffles me how married couples who are linked in so many ways work so hard to keep their financial lives separate. Especially when their earning levels are so unequal.

why don’t you just talk to him and come to an agreement? are you a partnership of equals? Why do you have to try and embarrass him into doing what you want?

She said he's a high earner so I doubt it. High earners can be very tight about contributing to DC. Some see it as the wife's responsibility with the wife and DC living frugally. While the husband spends money on himself like it's going out of fashion. I've been there so I know.

We are in this exact situation but I am the higher earner and her Dad kept on at me as to why I wasn’t adding to our DD’s savings account. He transfers £15 a month and has done since she was born. I reminded him that I pay for her tutoring, for all her clothes, for her holidays, for her activities, for her school equipment. Honestly, I feel like I am doing more than enough for her financially so maybe that is how he feels too?

Just do it when he's out at work!

This isn’t adding up, OP.
Either:

1. He has £2k left as a buffer at the end of every month. Ie, he’s not actually saving anything; just maintaining a £2k buffer at all times without growing it.
2. He’s saving £2k into his current account buffer each month, and at the end of the year he has a £24k buffer.

If he doesn’t want to save for them then he doesn’t want to save
Just accept it we didn’t save for ours
we took no board off them for the first year on the condition they saved that

Savings, then. If it’s not being spent, it’s being saved.