Wow.That was pretty gutsy of the parents to think they could still send a child to daycare but not to school. Pretty inconsiderate and clueless.
I have an area for sickness in my contract which says that I cannot properly take care of a sick child and also tend to the needs of the other children. I would hope that parents could understand that.
In terms of colds, I have written down that any green drainage or excessive drainage could be reason to send the child home.
You are not being too strict