Is it permissible for a breastfeeding mother to break her fast if her two three-month-old infants refuse formula milk? And what is the legal ruling for that?

If fasting harms a pregnant woman or her two children, there is no blame upon her if she breaks her fast. She must make up for the missed fasts (qada') if she broke her fast out of fear for herself. She must make up for the missed fasts (qada') and pay a fidyah (feeding one poor person for each day) if she broke her fast only out of fear for her two children.