HaleiVi, this is for you:
I was told, bsheym Rav Yaakov Kamenetzky zatzal, that the source for lighting one candle per child is that it used to be that after childbirth every mother was in the hospital for a minmiumum 10 days.
A similar idea is expressed by the Shu”t M’shaneh Halachos, as quoted by the Sh’miras Shabbos K’hilchasah. This is, in fact brought as proof that even missing b’oneis obligates an extra candle. The Mishna B’rurah doesn’t hold like this, though.
There’s a question on this approach; why would she add another candle for missing because of childbirth since her husband lit, and they were both yotzei?
I would suggest that a minhag might have developed for some, that a woman add an extra candle even if it was an oneis, and even if she was otherwise yotzei.
This would explain why some light extra even if not at fault for missing.
I’ve seen another explanation for the minhag of adding a candle for each child. The gemara in Shabbos says “haragil b’ner havin lei banim talmidei chachamim” (that the mizvah of neros helps one have children who become or marry talmidei chachamim), so as a z’chus, each time a child is born, a candle is added as a hiddur.
According to either of these explanations, a woman would not light according to the number of her husband’s children.