Work sickness

I understand all employees are entitled to a certain number of 'compassion' days. When I worked in a school this covered bereavement/and or any other life event at Head's/governers' discretion. It could also include child care. I think it was five days in an academic year.
I hope you feel better soon.

Everyone is entitled to time off to look after a sick child, but whether or not it’s paid is up to the employer. You don’t get any SSP for the first 3 days, I wonder if that’s why your employer has decided to do that?

Anyway, unfair as it may seem, it’s not breaking any employment law.

That definitely sounds unfair.
Apart from anything else, who's going to check that her child is actually the one that's ill anyway?
I think you're quite entitled to feel annoyed ?