On a sunny morning in early October, Joanna Coles, clad in a stylish tomato-red coat, and Ben Sherwood, dressed more demurely in a corduroy jacket, convened at their regular breakfast spot, the no-frills Star on 18 diner on Manhattan’s Far West Side.

The two veteran media executives were talking about their ambitious plans for The Daily Beast, the 16-year-old money-losing news website, in which they jointly acquired a minority stake in April.

But along with the predictable optimism about the mission they are taking on and enthusiasm about early signs of audience uptick and subscriber growth, Ms. Coles, a former chief content officer of Hearst Magazines, and Mr. Sherwood, a onetime president of ABC News and Disney TV chief, also conveyed a sense of frustration.

Frustration that they weren’t greeted by the staff they inherited as warmly as they expected. Frustration that the site’s tech problems meant they’ve had to buy multiple subscriptions just to log in. Frustration that convincing the newsroom of their editorial vision has been an uphill climb.

Less than three weeks after the pair’s takeover, New York magazine published a detailed report on the friction between reporters and Ms. Coles over story suggestions that they deemed ridiculous, including an investigation into whether former President Donald J. Trump was having stress-induced flatulence during his criminal trial and a list of the most obese members of Congress. (Neither article ran.)

It was clear that many of the sources for the report were inside the organization, with one unnamed staff member bluntly criticizing the new owners’ “warped vision” of the news site.