I used to have a parent text me at rest time every day to see how the day is going. I didn't have a problem with that.

I do what the above poster does. Parents may come early to chat with me at the end of the day. They are welcome to call me during the day, but I won't be answering and the same goes for after work hours.

I would let her know that you are not comfortable with being on the phone when you are supposed to be caring for children. I would let her know to come early if she wants to know about the day. I would let her know that I would not be talking on the phone after hours as well.

I realize you do not want to lose a client. I also realize that it looks like that may very well be the case. She has a sense of entitlement that is really over the top.