The morning drop-off maneuver where a parent gives their child a dose of fever reducer at 6:30 AM and drops them at your door at 7:00 AM is the absolute bane of our industry. By noon, the medicine wears off, the fever spikes, the child is miserable, and your entire classroom has been fully exposed.
You cannot afford to be soft on your exclusion policies. When you call a parent to pick up a sick child, stop apologizing. You are not inconveniencing them; you are protecting the health of the other twenty children in the room, plus your staff.
When they arrive, hand them a printed copy of the specific illness policy from your handbook. If a child has a questionable rash, do not try to diagnose it yourself. Require a formal doctor's note stating the child is no longer contagious before allowing them back in the building. Stand your ground. The healthy families in your center will silently thank you for it.