Reasoning behind אותו ואת בנו

Why women should hear parshas Zachor.

According to the Chinuch only men are obligated to hear parshas Zachor since it's the way for men to battle. The Minchas Chinuch says that it should also apply to women since, for an obligatory battle, even a kallah from under her chupa goes out to battle. The Rambam paskens this way as well.

Shu"t Binyan Tzion also argues on the Chinuch that, even if a woman doesn't battle, there is still the mitzvah of remembering Amalek, since they are two separate mitzvos. R' Noson Adler even made sure his maids would go and hear. 

In addition we can clarify that it's not a time bound mitzvah (that women are not obligated in,) since there is technically no set time for this reading, only Rabbinic decree.  However Shu"t Avnei Nezer does hold that its a time bound mitzvah, since you can not break Shabbos for the mitzvah to wipe out Amalek. However, the point of the Binyan Tzion, that there is a separate mitzvah to remember,still applies (even on Shabbos. So women are still obligated.)

Sharim Metzuyanim be'halacha