When i worked in Childcare, we would ask parents to collect a child if they had a constant green snotty nose. We would also ask them to bring in a doctors certificate the next time they came - to know that they weren't contagious. There are differing opinions of the green snotty nose - and many do say that it's the infection clearing. I guess when other parents see children walking around the centre with green snotty noses, they want to know why those children are there spreading their germs around.
It's really hard, because many directors do understand how difficult it is for the parents with regards to taking time off work.