Men making Kiddush (Shabbos day) for women after eating at shul

Question

Women and men are both equally chayiv in kiddush, at least on shabbos. Additionally there is a commonly known rule that a non obligated person (or obligated on a lower level) cannot fulfill a mitzvah on behalf of somone who is obligated. I’ve heard it said in the name of Rabbi Akiva Eger that men can make kiddush for women even after davening (and becoming only rabbinicly obligated) because in fact they're still obligated מדאורייתא because they intended not to "give up" their obligation.

But what about on Shabbos day, where they actually make kiddush in shul then go home? Then they aren't obligated anymore because they DID intend to get rid of their obligation and the women are still obligated rabbinically (it's day so it's not מדאורייתא).

So why the common Minhag for men is to eat kiddush at shul and still make kiddush for their family's at home?

Answer 1

I think you are confusing the different concepts. The discussion about a man being motze his wife on Friday night is a very different conversation to that of Shabbos day.

Friday night: This discussion revolves around the dispute whether arvus - the concept that one can exempt his fellow's obligation even after he has discharged his own - exists from a man to a woman (See Dagul Mervava and R' Akiva Eiger on Shulchan Aruch 271). A secondary discussion is whether a man is actually yotzei his own obligation during Friday night prayers, when he (a) doesn't mention Yetzias Mitzrayim, and (b) has no intention of being (or specific intention not to be) yotzei.

Shabbos day: This discussion is very different, because there is no need to factor arvus. Unlike Friday night, there is no bracha of Kiddush to make on his wife's behalf; the whole Kiddush is simply the regular borei pri hagafen. Any person who drinks grape juice or wine is obligated in this blessing too; as long as the husband drinks from the kos, this blessing is for himself as much as it is for her. Therefore, even without activating the mechanism of arvus, he can discharge his wife in her obligation using the concept of shomea k'oineh, just like he can be motzi her in hamotzi. Arvus is only necessary when the person making the blessing cannot make it for himself, but would like to make it on behalf of his friend.

Answer 2

R' Akiva Eiger in fact says (in Orach Chaim 271) that men can say kiddush after davening despite already having fulfilled their obligation, as in the first place they both have the same obligation. Those who argue (Dagul Mervava) maintain that there is a problem even on Friday night.