A Russian spy ring busted in the U.S. two years ago planned to recruit members' children to become agents, and one had already agreed to his parents' request, according to current and former U.S. officials.

When the suspects were arrested in 2010 with much fanfare, official accounts suggested they were largely ineffectual. New details about their time in the U.S., however, suggest their work was more sophisticated and sometimes more successful than previously known.

One...