Passfan: A married couple are counted as one person for being yotzei Mehadrin Min Hamehadrin by lighting Channukah candles. That is strange enough in its own right. There is no reason whatsoever why a daughter who is a Bas Chiyuv should not light for herself. None. She has her own Mitzvah and if the family wants to actually do Mehadrin Min Hamehadrin then she has to light her own (or her father lights a whole extra Chanukiyah for her if you want to use the way some Rishonim bring down the Minhag).
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