wow!

I know it isn't easy to just terminate. I personally would not have sent her an email about respect. The second the child threw up I would have called and said (in a not so nice tone) that you need to come pick up your child ASAP. When she picked up I would have said that my policy states 24 hours and that the child needs to stay home. I would not talk about it again later on, I would deal with it right at the moment. I updated my contract saying that failure to follow my sick policy could result in termination.

I had a parent once send their son to daycare sick. The boy threw up all over the table at snack time. I was fuming when dad picked up. I told him quite harshly that next time his son doesn't feel well he needs to stay home. It was maybe a month or so after that they gave their notice. Good riddance.