Is it allowed to refrain from fasting in Ramadan due to an illness and childcare?

It is permissible for an ill person who cannot fast Ramadan, to refrain from fasting. If possible, such a person is to make up the missed fast days after Ramadan. If the illness is chronic, it is obligatory to pay a fidya [compensation] which consists of feeding a poor person for each missed fast-day. This is based on the hadith of Ibn Umar (may God be pleased with them both) who narrated that the Prophet (peace and blessings be upon him) said: “Whoever dies with unperformed fast-days of Ramadan, then [the responsible family member] is to feed a poor person on his behalf for each missed fast-day” [recorded by Al-Tirmidhi and Ibn Majah].

In your case, it is permissible to refrain from fasting. And if your illness is chronic, you must feed a poor person for each day you do not fast the equivalent of 2. 75 kg of rice.

God the Almighty knows best