I have had cleaners who brought children with them, and wouldn't do it again. It was in the days when my own children were young, and I thought it wouldn't matter. It did.
Inevitably my children's toys were played with, and sometimes got broken, and I ended up feeding them all, which messed up my meal planning. I'm not sure that the children liked accompanying their parents either. As it worked out, though, my current cleaner used to come here with her mum, who has since retired. She managed to squeeze me in when I was looking for someone, as she remembered me, so it's all worked out for the best. She does have children, but her mum looks after them in the holidays or if they are off school sick.
I think in your circumstances I would ask her what she thinks should happen on the days she can't make it. Obviously a child in hospital is a different matter, but there may be a way round the school holidays situation if she knows how annoying it is for you when she can't make it.