If you plan on spending you're remote working hours supervising children, your not really working. Working at night will not allow more time to supervise children during the day.
I'm not convinced the OP was suggesting that limiting women's rights was a solution, merely that increased female labor participation will result in less time spent with children.
> There are plenty of good solutions that would work well
I'm not sure there are many.
> progress we've made towards equality
We've made progress in some areas, and regressed in others.
This is an issue about the amount of available time. Focusing more time in work will divert time from other activities. There is no other way of looking at it.
edit:spelling
Remote working means you don't waste time commuting, you can be available during breaks because you're already at home, and you can step away from your keyboard and be there immediately in an emergency. All those things are huge benefits over office work if you have kids.
Changing core hours doesn't mean working nights. It means things like starting at 6am and finishing at 2pm, so you're available to look after your kids in after school hours, or starting at 10am so you have time to take your kids to kindergarten. Or, as you say, working at night so you can be there all day (if you're one of these lucky people who don't need much sleep.)
There are solutions to this problem.
Massively increasing the supply of housing so a parent regardless of gender could stay at home and still afford a house would also fix the problem.
A universal basic income would also fix the issue of both parents needing to work to afford a house.
We could also consider parenting a job and pay parents a living wage to stay at home and raise their kids.
The fact you immediately suggested the only solution to this problem would be to limit women's right to work is a bit sad. There are plenty of good solutions that would work well and don't need to restrict or rollback the progress we've made towards equality. At the very least you could have suggested limiting families to one working parent rather than specifically women.