[A woman not returning with her daughter to the doctor]

The answer – and Allah is the One who grants success – is that the mother is not liable for diyah or kaffārah in this case. The excuse that prevented her from returning to the doctor lifts the sin from her. Were it not for the presence of the excuse, she would have been sinful. This is because it is obligatory upon the guardian of the small child who does not know how to attend to his own interests to carry out everything the child needs in terms of food, drink, clothing, cleanliness, treatment, and what is connected to that.
What indicates that this is obligatory upon the one who has custody of the child is His saying, exalted is He: “Mothers shall breastfeed their children for two complete years – for whoever wishes to complete the nursing period… until His saying: “…then if they both desire weaning by mutual consent and consultation, there is no blame upon them” [al-Baqarah:233]. This verse indicates the obligation of nursing the child for two years, and that it is not permissible to wean him before the two years except after mutual consent of the parents and their consultation concerning the best interest of the infant in being weaned.
That indicates that it is obligatory to take into account the child’s interest in nursing by the indication of the verse, and in matters other than nursing by analogy.

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2