I wonder if they medicated her in the morning and that is why she seemed fine at drop off but then got worse as the morning progressed.....
I would also not appreciate the threats.
I have never sent home due to a 'cold'. BUT if the child is clearly 'zoned out' and not wanting to participate and needs one-on-one care then I would expect you to call parents. They shoudl have empathy for their child and know that this comes along with being a working parent. Sometimes they need you at home with them, in jammies.