What is the ruling on praying in a prayer nook established in a house that is disputed among heirs, and the ex-wife of the deceased homeowner, who left behind another wife and children, relinquished her claim to it?

The basic principle is that prayer is valid in any pure place, even in a usurped place, though it entails sin according to the majority of scholars. If the divorced wife owns the house through a valid gift and she is of sound mind and grants permission to pray in it, then prayer in it is permissible. If there is a dispute over the house, it is advisable to refer the matter to the Sharia court to determine the rightful owner. Nevertheless, prayer is valid even if the place is usurped, according to the majority of scholars.