To whom would custody of the two children go if the wife, afflicted with a rare and incurable disease that necessitates her frequent hospitalization, were to request a divorce?

If the wife's visits to hospitals do not affect her ability to custody and care for her two children, then her right to custody remains. However, if she is unable to care for their affairs, this nullifies her custody, because the custodian is required to be capable and competent, and an incapacitated person cannot be a custodian. In the event that the mother's custody is forfeited, the right transfers to the next in line according to the order, and it is advised to refer the matter to the Sharia judge to consider the mother's suitability for custody.