An unlikely custody battle has broken out over a stash of Norman Rockwell art allegedly stolen and hidden for decades—in the White House. In 1943, Rockwell created several sketches and watercolors chronicling a typical day in the White House’s executive wing, depicting everyone from senators to soldiers sitting on red sofas and chairs as they waited to meet President Franklin D. Roosevelt. The resulting montage, “So You Want to See the President,” ran in the Nov. 13, 1943, issue of “The Saturday Evening Post.” Rockwell gave the four original works on paper from that assignment to FDR’s longtime press secretary,...