In late October 2017, Jared Kushner, President Trump’s son-in-law and Middle East adviser, dropped into Saudi Arabia for an unannounced visit to the desert retreat of Crown Prince Mohammed bin Salman, who was in the process of consolidating his power. The two men talked privately late into the night.

Just a day earlier, Mr. Kushner’s younger brother, Josh, then 32, was flying out of the kingdom.

Jared came to talk policy, but Josh was there on business.

The founder of an eight-year-old venture capital firm, Josh Kushner had spent the three days before his brother’s arrival at an investor conference, where Prince Mohammed had promised to spend billions of dollars on a high-tech future for Saudi Arabia.

As others sat through speeches in a gilded conference hall, several participants said, the younger Mr. Kushner frequently ducked out for more exclusive conversations with Saudi officials.