Are there any sources for a woman when lighting shabbos candles to light one candle for each member of the family?
It is interesting that lighting extra candles for each child has become a prevalent custom, despite its sources being relatively obscure.
She’eris Yehudah (21) writes that he knows no reason for this custom. However, Likkutei Maharich (Vol. 2, seder hanhagos) writes that the custom of women is to add an extra candle for each child that is born, and writes that the source for the practice is the teaching of the Gemara (Shabbos 23b) whereby those who light many candles merit to have children and sons-in-law that are Torah scholars. Therefore, for each birth a candle is added, so that the child (or the future son-in-law) will become a Torah scholar.
See also Mishnah Halachos (7:35) who suggests two alternative reasons for which an extra candle is added for each birth. One is on account of the missed lighting of Shabbos (for a baby who is born around Shabbos; this reason is strained, for a woman who misses candle lighting due to extraneous circumstances (oness) does not need to add another candle). The other is by comparison with the ruling of Rambam concerning Chanukah candles, according to which one lights the number of candles corresponding to members of the household (why this comparison should be made is unclear).