Am I counted among those who fasted Ramadan when making up for missed days due to menstruation, and how can I perform good deeds alongside the responsibilities of motherhood and childcare?

All praise is due to Allah.

Whoever breaks their fast in Ramadan due to an excuse and then makes up for it, they will have a reward similar to that of fasting in Ramadan, if Allah wills, based on the hadith: "When a servant falls ill or travels, what they used to do while healthy and at home will be written for them." So, the one with an excuse has the ruling of a fasting person, and they are hoped to receive the full reward if Allah knows from their heart that they would have performed it had it not been for the excuse. A righteous woman should balance her household duties and worship by organizing her time and committing to it, joining collective programs and associating with righteous women, and perhaps spending money to dedicate herself to worship. Among the helpful means are: reciting tasbeeh (SubhanAllah), tahmeed (Alhamdulillah), and takbeer (Allahu Akbar) before sleeping. So, let her seek help from Allah the Almighty, organize her time, and be keen on good companionship and beneficial programs.

And Allah knows best.