I think OP's clarification that she is the main breadwinner makes a real difference here IMO.
And I totally refute that people were being sexist by asking that question or even assuming that her DH was, because we were given working hours and it is highly
unusual (though not impossible) that a person working from 10:00-4:30 is the main breadwinner irrespective of gender.
Typically part time hours mean a reduction of income. This is hopefully agreed to by both partners to facilitate a certain lifestyle benefit, often (but not always) based on someone being at home with the children.
If the OPs part time hours were being facilitated by her partners extremely long hours, then I think it would have had to be a very tricky conversation, which included the possibility of the OP going full time and the OH going part time to care for all his children.
HOWEVER, OP has said that she is the main breadwinner. So it's a very different situation, and categorically unfair that she's being asked to shoulder the majority of the childcare / home admin and financial contribution. That's obviously a no go,
It's worth mentioning that the OP is on Mat leave at the moment. So all the posters frothing at the mouth that her husband isn't pulling his weight in the current scenario are talking nonsense. OP said he's very hands on with the kids on the weekends, and I don't think it's that surprising that a parent on mat leave does the majority of the working hours care.
However, when OP returns to work things change dramatically, doubly so as the OP is the primary breadwinner. While her hours are better for children, the fact is she doesn't want to have to manage DSS on weekday evenings.
I still strongly believe that it is the kids home and that means that a weekend only rule doesn't work. I also strongly believe that any child told they are only allowed to visit at weekends would not feel like a member of the household but an unwelcome guest. And a child that knows OP is home from 4:30 but has been told that his coming home mid-week isn't allowed might (rightly or wrongly) interpret that as rejection by his stepmother.
In some ways (specifically for handling this really) your part time but breadwinner status is a pain in the arse. Because if you were out at work you wouldn't be available and your husband would either have to flex his hours or sort childcare. The same is true now BUT you are at home which makes things feel more awkward.
Giving the business isn't bringing in money, and he has childcare responsibilities that you're unwilling (quite fairly) to shoulder for him, I think he will have to shelve the business for now and get a part time job that allows for him to care for all his children (including your shared one).
It sounds like this won't have any impact on finances as the business is fledgling and not making a lot. If there is a small financial impact, hopefully this will be covered by reduction in CM (as having more overnights) or it will have to be absorbed by the family generally.
So YWouldBU to say they can't come more. But you would absolutely NOT be unreasonable to say that he needs to facilitate this, and that actually he needs to rethink the business generally as it is not working in terms of his contributions to family life anyway.