Saying hello to the daycare child and parent is your job not your daughter's job. She just lives there. It is no different than when the second or third child arrive do you make all of the early arrivals dutifully line up and in chorus say hello - I hope not.

I get that the parent thought your child was just being rude and ignoring them and ok time difference means new routines for everyone so parent will also have to get used to the idea that your child needs some space in the morning before she is ready to interact with anyone.

The mom was out of line to say something. Her daughter is not the most important person in the daycare.