Is a man permitted to divorce his wife for refusing sexual intimacy, claiming illness or childcare as a pretext?

There should be no haste in divorce, for it is the most detestable of lawful things to Allah. Rather, one must investigate the reasons for the wife's refusal of the marital bed and address them, whether it be a physical or psychological illness, or a touch from jinn or sorcery, by treating it with the Quran and supplications.

If it becomes clear that she is free from all of that, then she is disobedient (nashiz). Her disobedience should be addressed through admonition and discipline. If that does not work, and he cannot marry another woman except by divorcing her, then he should divorce her and seek another wife who will preserve his chastity.