What exactly are women’s tefillah requirements, especially if there are children in the house? What about hearing laining on Shabbat, coming to shul after Chazarat Ha’shatz and most importantly requirements to hear Mivorchim Hachodesh B’tzibur? Thank you.

Best would be for women to daven Birkot Hashachar, Birkot Hatorah and twice a day Amidah for Shacharit and Mincha. If that is difficult once a day Amidah is enough, preferably Shacharit. Women who have little children to care for and find no time for Amidah can fulfill their obligation with Birkot Hashachar and Birkot HaTorah alone. Women have no obligation [though are more than welcome] to daven with a Minyan or to listen to the Torah reading in shule [as the Halacha is not like Magen Avraham] how much more so they are exempt from the Birkat Hachodesh. [See Pninei Halacha Tfilat Nashim pp. 21-23]