Among the most fascinating parlor games during President Donald Trump’s first six months in office has been gauging the political influence wielded by his family member-advisers, Ivanka Trump and Jared Kushner. Sometimes, it appears as though the two have the sort of power that one might more normally expect in a kingdom, petrostate, or banana republic. Earlier this month, for instance, Ivanka Trump raised eyebrows when she represented her dad on stage at the G20 in Hamburg; Kushner, for his part, set off similar curiosity when he traveled to Iraq and Israel as a representative for his father-in-law’s administration. At other times, however, it appears as though the second First Couple has considerably less juice. Last week, after all, Trump’s tweet disavowing transgender individuals from serving in the military caught Ivanka and Jared completely off guard, according to a person familiar with the situation. Ivanka, in particular, has been publicly and privately advocating for L.G.B.T. rights.

Perhaps nowhere, however, has their influence been more subtle, and ultimately, more effective, than in the strange case of Anthony Scaramucci. The Mooch, as he is known, came on board as the White House’s communications director 10 days ago, with the full backing of the Trump-Kushners. It was Ivanka, after all, who sat alongside her father in the Oval Office on the eve of the official announcement of the Mooch’s ascendance, even as other senior White House aides, including former press secretary Sean Spicer (who resigned immediately after his appointment), former chief of staff Reince Priebus (who blocked Scaramucci’s appointment to various White House roles for months and resigned last Friday after public, profanity-laden lashings from the Mooch), and Stephen Bannon (who, despite his dismay, still remains in the West Wing), urged against the decision.

Kushner and Ivanka’s initial support for the Mooch, the kind of guy who would later describe Bannon as an erotic gymnast and Priebus as a “schizophrenic paranoiac” in a phone conversation with a New Yorker reporter, does not ostensibly jell with the meticulous, modern Orthodox, tailored-suit-and-updo image that the Trump-Kushners project. But the Mooch and the Trump-Kushners shared two important traits: an unyielding loyalty to Trump and a burning desire to see Reince Priebus go. For months, the Mooch had been feuding with the now-former chief of staff, who had blocked him from a role in the West Wing since January. (The Mooch described their relationship as brotherly when he first took the job; less than a week later, he clarified that they were brothers like Cain and Abel, where Cain killed Abel for God’s favor.) Less publicly, Ivanka and Jared had also been diligently pushing for Priebus’s ouster, according to a White House official.

All three got their way last week, when the president tweeted on Friday afternoon that Priebus would be replaced by retired general John Kelly, who had been serving as his secretary of homeland security. Kushner and Ivanka were thrilled with Kelly’s appointment, the White House official added, sensing that Kelly could professionalize a West Wing in need of a management change. They supported and empowered him to call the shots to make staffing and structural decisions. On Monday afternoon, Ivanka tweeted, “Looking forward to serving alongside John Kelly as we work for the American people. General Kelly is a true American hero.” They both sat behind President Trump as he told his Cabinet that Kelly “will go down, in terms of the position of chief of staff, one of the great ever” in a meeting this morning. By the afternoon, White House press secretary Sarah Huckabee Sanders said that all White House staffers would report directly to Kelly.