Being an akeres habayis has nothing to do with whether the mother puts tefillin, goes to minyanim, learns rashi and tosfos, etc.
A woman doesn’t have to do any of that because of her innate kedusha. Mothers ignite the sparks that are waiting to be kindled within the hearts of the next generation. Mothers nurture the soul of each child teaching them the meaning of endless love. Mothers carry life, give life and shed tears as they pray that each child lives a purposeful and good life.
That is the role of the yiddishe mame.
The tateh is the one who learns and davens.