Besides Flashman it is not about the girl being rude to an adult customer, upsetting the OP, etc -- it is more about the fact that she addressed these comments to a young child who was already in a potentially embarrassing situation. It could have a lasting effect.
Personally I don't think being sacked is that harsh a punishment for young person anyway, it's not like it's the end of her career or she has four kids to support (presumably!). It's an opportunity for her to learn a lesson and she will, if so minded, easily find another job. Shop jobs etc are not hard to come by. Unless you insist on psycho swearing-at-babies behaviour.