The White House faces a “very ugly” legal battle with Amazon over the handling of a massive contract to handle the Pentagon’s vast cloud computing needs, experts say, and top administration officials ultimately may have to reveal under oath whether President Trump personally interfered in the process. The fight is already shaping up as a battle of economic and political super heavyweights, with Mr. Trump making clear his lack of respect for Amazon founder Jeff Bezos and his business empire, which happens to include The Washington Post. The Defense Department last month awarded the 10-year, $10 billion military cloud computing...