HANOI — President Trump spent Wednesday here in Vietnam cozying up to North Korean leader Kim Jong Un over grilled sirloin and chocolate lava cake and reaching for the legacy he wants: the great dealmaker negotiating a historic nuclear arms accord.

But halfway around the globe, an entirely different legacy for Trump was thrust to the fore by his longtime personal attorney and fixer — that of an alleged con man, liar, racist and, ultimately, criminal.

Michael Cohen’s explosive testimony to Congress was not only potentially humiliating for Trump. It also portrayed the president as an unreliable and dishonest man at the very moment he is conducting diplomacy with the world’s most erratic and untrusting dictator. And it propelled Trump’s presidency into greater legal and political peril.

On a day when two events of potentially lasting importance played out simultaneously some 8,300 miles apart, the spectacle in Washington overwhelmed the one in Hanoi....