http://revach.net/article.php?id=3364

Section: Halacha   Category: Tshuvos
Noda B'Yehuda & Rebbi Akiva Eiger: When Father Is Away Who Should Make Kiddush, The Mother Or A Child?
Since a woman is obligated in Kiddush Min HaTorah, a katan cannot be motzi her. However says the Noda B'Yehuda (Dagul MeirvavaOC 271), if the women davened Friday night than she was yotzei herchiyuv min hatorah by saying Vayichulu in Shmoneh Esrei.  Now her obligation to make on wine is only M'D'Rabanan so the child who is also chayav M'D'Rabanan can be motzi her.  However he says, if the child also davened then he has a double D'Rabanan and once again cannot be motzi the women who has only one D'Rabanan.  Rebbi Akiva Eiger argues and says that even if the Katan is a double D'Rabanan he may be motzi a women who is a single D'Rabanan.

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