I can't see why this is 'punishing' the child. There are lots of children in blended families, and others who have lost a parent. The ex isn't saying she doesn't want anything to do with the child, just that she doesn'nt want to be called her mother - because she's not her mother and she's not really her new stepmom since she and the father aren't together.

It's sad, but it's not cruel.