However, if a women has sick child for example, day worked from home is paid 50%.
This sounds like a favor measure from the employer. Normally, if you have to stay home for a sick child, you need to take social leave, which is not paid at all.
Normally, if you have a sick child at home that needs taking care off, you should not be able to do your job for 100%.
Even worse, next Monday it is national strike and many women would work from home and school are also not going to work. Women with children will be paid 50% (even children are healthy) and other women and men would be paid 100%.
Nobody is obliged to stay at home, I think? So nobody forbids your wife to just come to work and be paid at full, no?
Only problem I see is indeed the arbitrarity here. From one part, I do understand that the employer assumes that you can't work for 100% with children in the house, but from the other part, who sais you can't work for 75% or even 80% instead of 50%?
How will the employer describe this on the payslip? Will women with children have 1/2 day off social leave or something like that? What's the official policy around home work at your company (apart from the reason why)?
If, for instance, people can work 1 day a week from home at full pay, then your wife has the right to do so on monday, without having to mention to the employer that the reason is that the school is on strike. She will have to work 100% that day, however (kids go to the grandparents or something like that).