This time the OP gets to herself......this is after ensuring dc get to school, being available and doing pick ups, being there in case the school phones, being there if one is ill, all the housework, shopping, cooking.....can't overestimate all that with 4 dc.
I think it's a shame the adults don't see much if each other (well, every weekday evening from about 6pm apparently doesn't count?) But the OP has a right to a life too and if she enjoys the job and finds it fulfilling then I think she should persue it.
It's unsupportive of him to suggest she stops or reduces it. She can't do weekdays due to kids and the holidays, and the illness days (might be out of line here, but doubt the DH will come home from work to pick up an ill child).
And of course they can't put the kids in a holiday club so she can work weekdays, there's no way her earnings would make it worthwhile (sorry OP).
But they do need to work together to resolve it.
They both get paid annual leave and they need to plan and make judicious use of this for the next year or so, until the dc are a bit older and a bit more self-sufficiant.
It's not fair for men to insist that women remain at home and continually erode their independence and ability to support themselves.