The Trump White House has frequently been called chaotic, wild, undisciplined, disorderly. But a better word might be “unruly,” because if there’s one thing Donald Trump can’t abide, it’s rules. Not only has the Trump administration signally failed to follow the rules, it’s not clear it ever bothered to learn them. But as the Democrats took control of the House of Representatives last week, that abruptly changed. Trump is about to get schooled in the rules of the game.

For two years, thanks to a Republican Congress that chose not to honor its constitutional duty to maintain oversight of the executive branch, the American political drama has centred on special counsel’s Robert Mueller’s investigation. But that focus is about to widen, as Nancy Pelosi, the once and future Speaker of the House, reclaimed the gavel, promising to show Americans its power: the picture of her smiling as she wielded it went viral, for good reason.

That the game has changed, significantly, was clear in the many stories and images circulating last week: as the first two Native American women sworn into Congress tearfully embraced; as Ilhan Omar became the first woman to wear the hijab in Congress and Rashida Tlaib was sworn in on her own Quran; as Kyrsten Sinema became the first openly bisexual woman to join Congress, and swore her oath of office on the Constitutions of the United States and her home state of Arizona, rather than on a religious text; and as Alexandria Ocasio-Cortez responded to a failed attempt to shame her for once having danced on a rooftop in a tribute to The Breakfast Club by dancing into her congressional office.

Pelosi began by sending the president a brief letter, instructing him to deliver a State of the Union address on 29 January. It opened by reminding Trump of the rules that are about to be enforced: “The constitution established the legislative, executive, and judicial branches as co-equal branches of government.” Some commentators called this sentence gratuitous and for any other president it would have been. But this one has more than earned a civics lesson, given that he notoriously claimed as he entered office that Congress works for him. Certainly, the Congress he’s enjoyed until now, under Senator Mitch McConnell and former Speaker Paul Ryan (who just left office with a dismal 12% approval rating), gave him reason to think so, and McConnell continues to do so.

Play Video 1:17 Tears, hugs and dabbing as new Congress sworn in – video report

Pelosi’s first action was to summon Trump to Congress at her behest. The message was clear: this is her territory, and she’s in charge now. Refusing to fund Trump’s signature promise of a wall on the southern border, Pelosi called it a barrier not “between America and Mexico, but between reality and his constituents, his supporters”. Pelosi will reintroduce the Trump White House to reality, putting serious brakes on what is increasingly a runaway train. One way to do that is through non-partisan strengthening of the electoral process and Democrats introduced a bill that calls for automatic voter registration, nationwide early voting, ending congressional gerrymandering and the release of presidential tax returns.

But Pelosi is also asserting the power of her office, going so far as to claim in one interview that the constitution makes her office equal to the president’s. This is untrue: Congress in its entirety equals the presidency, while she only leads one of its two chambers. That said, Pelosi has just, not incidentally, become third in line to the Oval Office; should something occur that occasioned the removal of both the president and the vice president from office before 2020, Nancy Pelosi would by law assume the presidency.

But what might such a something be? Many Americans think Congress, which can remove the president, is spoiled for justifications. One freshman member of the 116th House, the most diverse in American history, lost no time in saying so. Palestinian-American Tlaib caused uproar when she celebrated her accession to Congress by telling advocacy group MoveOn that the House would “impeach the motherfucker.”

Many Americans think that Congress, which can remove the President, is spoiled for justifications.

That is not currently the position of senior members of the House; Pelosi has made clear that she awaits the outcome of the Mueller investigation before deciding whether to bring impeachment proceedings. Nor would impeachment guarantee Trump’s removal: the House votes whether to impeach, but the Senate votes whether to expel and it’s hard to imagine McConnell’s Senate doing any such thing. Certainly not as matters stand.

But that’s also where things get interesting. The Democrats now control oversight and investigations, with subpoena power. On her second day, Pelosi denounced the “culture of cronyism, corruption and incompetence” in the Trump administration, including, she specified, the personal enrichment of individual cabinet members. For two years, numerous ethics scandals have passed by a Congress that barely exerted itself to shrug; now, Democrats chair the committees of jurisdiction and have the power to jail those who defy subpoenas. That power has not been exercised in almost a century, but every weapon in the congressional arsenal may be needed to stop a president who weaponises reality itself.

House Democrats’ oversight and investigatory powers are much broader than Mueller’s very specific investigation into the Trump campaign’s possible collusion with Russia. They have announced their intention to follow the money and can rigorously investigate not only Russian electoral interference, but also the Trump family’s financial ties with foreign governments, including Russia and Saudi Arabia, and the possibility that those financial interests are influencing the administration’s policy; money laundering; ethics violations; abuses of power, including profiting from the presidency; and obstruction of justice. They can investigate Trump’s personal finances, and demand his tax returns; if he refuses, they can take it to the courts. In addition, they have promised to scrutinise the legality of some of the administration’s more controversial policies, including the separation of immigrant families at the border. Should the president fire Mueller, they can reappoint him as independent counsel. Any of these investigations might seriously change the picture regarding impeachment.

Facebook Twitter Pinterest New Democrats at the Capitol last week. From left, Alexandria Ocasio-Cortez, Ilhan Omar and Haley Stevens. Photograph: Saul Loeb/AFP/Getty Images

The House committees can also turn over evidence they uncover to the Department of Justice for prosecution, which may change the DOJ’s position on whether to indict a sitting president. The DOJ is obeying a directive – not a law, but an internal procedural memo – stating that, in general, a sitting president should not be indicted, for the simple (and good) reason that this could usurp congressional oversight. According to the directive’s logic, if a president breaks the law, Congress should impeach and remove and then the Justice Department can decide whether to indict an ordinary citizen. But these investigations raise significant questions about whether Trump became president illegally or thanks to criminal activity; in such circumstances, according to many legal experts, including the former US Solicitor General Neal Katyal, the Justice Department is not bound to follow this “general” directive.

Donald Trump has long believed that the rules don’t apply to him, but that’s only because they haven’t been applied to him. The likes of Omar, Tlaib, Sinema, Ocasio-Cortez, and their male freshmen colleagues, will hold Pelosi to account, as well as Donald Trump – about whom we can finally stop asking when the game will be on and start asking when the game will be up.