In times gone by, the new mother would stay in hospital for a number of days following birth, and would generally not be in a position to light שבת licht the first שבת following the birth of a child. Therefore the mother has a din of one who forgot to light, for which the הלכה is that they must light an extra candle every week for the rest of her life!
I've always had difficulty with this idea.
The general rule, of course, is oneis rachmana patrei -- if a person is in an unavoidable circumstance, he or she is exempt from the mitzvah -- and there is no punishment. A classic example would be someone who is stranded on a deserted island and cannot get matzah for pesach. Since he cannot get matzah, he is an oneis and is patur.
I would imagine that being stuck in the hospital is also a situation of an oneis, whether it's because one had a baby, or for any other life-threatening situation. As such, I don't see how she should be subject to a kenas for failing to light.
Furthermore, the mitzvah to light is primarily on the household, not on the woman herself. If a man lives alone, for example, he is required to light. As such, if she's in the hospital and her husband lights for her, I furthermore cannot see how she should be liable for a penalty.
That's not to say that the practice of adding an additional light when a child is born is not proper. It is a custom that has gone back centuries or more. I think, however, it's possible to look at this phenomenon of adding a light for having a baby or forgetting to light as two separate events:
1. There is a custom that if a woman forgets to light (through negligence or willful misconduct), then she should add a light as a penalty/reminder.
2. If she has a baby, she should add a light -- not as a penalty, but rather because there is a custom to do so.