SINGAPORE — Two years after his death, no memorials, statues or streets in Singapore are named after Lee Kuan Yew, who established this city-state as a modern nation and built it into a prosperous showcase for his view that limited political freedoms best suit Asian values.

Now a bitter and public family dispute over the fate of his modest house has shattered Singapore’s image as an orderly authoritarian ideal and hinted at deeper divisions about its political future.

Two of Mr. Lee’s three children have accused their elder brother, the prime minister, of abusing his power to preserve the house against their father’s wishes. The motive, they said, is to shore up his own political legitimacy and ultimately to establish a dynasty for which he is grooming his son.

These charges have transformed what on the surface is an ugly estate battle into a national crisis that has raised questions about how this island nation is governed, the basis of the governing party’s uninterrupted 58-year rule and how the country’s leaders are chosen.