Is it permissible for a sick woman who is unable to make up for the missed fasts of Ramadan on normal days due to preparing food for her children, to break her fast in Ramadan and feed a poor person for each day instead of making up the fast?

Mere feelings of tiredness and hunger from work are not a valid excuse for not making up missed Ramadan fasts. If a woman is able to fast in Ramadan, she is also able to fast at other times. Ordinary fatigue is not considered an excuse under Islamic law, and she must make up the fasts. The hardship that is considered valid under Islamic law is severe hardship that is feared to harm the person, or organs, or cause illness. In this case, breaking the fast is permissible, with the obligation to make it up later. This woman is permitted to delay making up the fasts until winter, but she is not permitted to delay without a valid excuse until another Ramadan begins. Whoever does so has sinned and must make up the fasts and feed a poor person for each day.