MIAMI — The donations kept pouring in: hundreds of thousands of dollars in campaign contributions to President Obama and more than a dozen members of Congress, carefully routed through the families of two wealthy brothers in Florida. They had good reason to be generous. The two men, Roberto and William Isaias, are fugitives from Ecuador, which has angrily pressed Washington to turn them over, to no avail. A year after their relatives gave $90,000 to help re-elect Mr. Obama, the administration rejected Ecuador’s extradition request for the men, fueling accusations that such donations were helping to keep the brothers and...