If a parent made a comment to me like that, I would have terminated them on the spot. There is no respect there. Also, in order to provide the best possible care for their child, you need to have a decent relationship with parents in order to communicate about any issues. Unfortunately, this doesn't sound like it's possible. I would advertise the spot immediately.

However, if you choose not to, then I would make sure to be firm with the three year old, but pick your battles...don't worry if she doesn't say hi to other people...that can come later. Right now, it sounds like she is feeling very insecure and needs time to adjust to her brother just starting school and not being there. When she has a fit when her brother goes to school, just try leaving her be. I had a child like this and he was better left alone for a little while. If I tried to approach, it would make things worse. So try leaving her alone and ignoring the crying. She needs to learn to self sooth. Some children aren't comforted by other peoples hugs or talk, some just require their own space.

I wish you luck.