OP, this is abuse. The big thing here is the assumption on his part that what he brings in is his and what you bring in is his to control.
As with all other types of abuse, you are feeling the emotional and psychological effects of it.
The biggest effect is that you feel you have no options either short term (you can't go against his edicts about where you should shop) or long term (you can't make plans to work since he will not compromise his hours at all to allow you to develop a career or hold a job, and he will not contribute to child care, so you are stuck).
Please contact Women's Aid. 0808 2000 247. Leave a message if you don't get a person on the line immediately.
You are not an equal in this relationship. He has turned it into a hierarchy with him at the top and you treated like an exploited housekeeper/childcare worker.
This is not about budgeting. It is not about money at all.
I suspect it is about the H finding a handy way to play the role of master of all he surveys. He would find some other way of grinding the OP down if he wasn't doing it financially.
The other possibility is that this is a case of anxiety run amok on the part of the H, and if so then he needs to seek urgent help from a therapist, because he risks losing his wife and children over this. OP, do you feel you could sit down with him and have a conversation where you would challenge him with this?
If not, what holds you back?
A few other questions:
Your money from your business goes into one account - how is tax assessed on your business?
Is this one account a joint account and if so are both your names on this account? Do you both have access to online banking associated with this account?
Do you or your H have a credit card? Whose name is on the CC account if any?
Is there a savings account or any brokerage accounts, or any assets like flats that are rented out?
Who handles mortgage, car payments, car maintenance/repairs, insurance (home and car and life insurance, private health insurance if any) - including research and pricing of these financial products, deciding where to go on holiday, decisions on private or state school for children, activities for children, your clothing and footwear and health/dental access?