No OP, that doesn't sound right at all.
You're going to need to make a list of all bills, food, clothing etc which are regular monthly bills.
Then a list of 'nice to have's' i.e Takeaways, holidays etc.
You then look at what your wages/benefits are monthly. (Don't forget to add extra for your pension contributions as you're missing out on that by being part-time, but being part-time also saves on childcare, so to avoid you having less of a pension due to caring responsibilities, you need to pay extra in).
You add the total bills and 'nice to have' spends as well as the non changing regular bills.
You put the bills money into a new joint account every month and savings (for hols/takeaways etc) into a separate account.
All bill/food/kids & school clothing & activities gets paid for from the bills account. All takeaways/holidays gets paid for from the savings account.
Whatever money is left from both your wages then gets split, £x amount each for personal spends (NOT for kids stuff etc) and the rest split for you both to have personal savings.
It's the only way that you're both actually paying for 'family' expenses fairly as well as getting personal spends and personal savings.
(Personal savings I wouldn't disclose to a spouse who didn't also save. Once it's in 'your' savings, it's no longer 'family' money imo. Too many women end up paying for all the kids clothing/activities etc simply because they are the ones booking or taking them to sports/classes and taking them shopping & buying their clothing when the kids have grown etc!)