I dont send kids home for a runny nose. Thats part of group care in the winter. If there was vomiting, a fever or uncontrollable crying associated with the running nose then yes I would. If the child was coping well, as others have mentioned, I would have left them. I also wanted to point out that this is a good time to be teaching your dck proper coughing and blowing their nose techniques. At 20 months, she is perfectly capable and then it relieves some of the stress on you