Vladimir Putin did not like the prying.

It was 2008, and the Russian president, then 56 and eight years into his tightening grip on power, stood for a news conference in Sardinia’s lavish Villa Certosa. At his side was his closest ally in Western Europe, Silvio Berlusconi, the media mogul and Italian prime minister of legendarily hedonist appetites with whom he shared a taste for raunchy jokes, over-the-top furnishings and vast wealth.

During the summers, Putin’s two teenage daughters had the run of the sprawling villa, going on secret luxury shopping and boating excursions under strict orders that their identities remain concealed and their faces hidden from cameras, according to a person with knowledge of the arrangement.