On a single day in December 2015, Gary Jones, who resigned last month as president of the United Automobile Workers, spent more than $13,000 of the union’s money at a cigar store in Arizona. His purchases included a dozen $268 boxes of Ashton Double Magnums and a dozen boxes of Ashton Monarchs at $274.50 each. “Hi Gary, Thank you & Happy New Year,” read a handwritten note from the store. The purchases, documented by a federal complaint filed against a union leader in September, were part of more than $60,000 in cigars and cigar paraphernalia that Mr. Jones and other...