YANBU.
This argument from fathers gets me every time. They don’t seem to think caring (for children or anyone else) and housework is actually work. Especially in school holidays or when the kids are sick, when you look after them all day. He’s been at work all day - well so have you! You work split shifts.
Presumably, you’ve made dinner before you go out. So, what’s he objecting to? Getting his own kids ready for bed twice a week? And they’re presumably not too challenging to get to bed at primary age.
If he were a lone father (e.g. in the case - heaven forbid - of bereavement), he’d have to pay someone to do all the housework 5 days a week, household admin, get the kids ready for school, look after them after school, make dinner and get them settled in bed, e.g. a housekeeper/nanny. Would they not be entitled to two evenings off a week?
Or, like many lone parents, he’d have to do the whole lot himself. No evenings off. No days off. Juggling childcare, running a family household and a full-time job week after week, month after month, year after year. For decades. Welcome to my world! There were many evenings when my kids were younger when I had to log back on after dinner and bedtime. Believe me, if he was suddenly having to do that, as (hats off to them) many lone fathers do, only being responsible two evenings a week for two hours would be bliss.
I have two close friends who became lone fathers because their partners died or are in residential care and another who cares at home for his severely disabled partner following a stroke, as well as doing all the above. None have family support. Believe me, when men have no choice to step up, funnily enough they suddenly can.
Maybe draw up a contract of employment for yourself: hours, pay and working conditions. Then he might see what value he gets from your hourly rate. And you can work to rule!