Don't you have a 24 hour rule for illness? In my daycare the one who was sent home with the runs could not have returned the next day anyway, has to be 24 hour symptom free- and actually if I sent them home sick it's 48 hours. (made that rule to encourage them to keep them home in the first place when sick)
It's beyond disrespectful for them to be so Meh about sending a child they knew was sick- it disrespects you, your family and every daycare family enrolled.