To the political right in America, Joe Biden’s son Hunter has been the gift that keeps on giving, with his public struggles with addiction, scandalous private life and tangled business life. To the left, Hunter’s travails are dismissed as a Republican political obsession and a talking point for tabloid journalism and internet gossip.

But last week, two witnesses called before a federal grand jury seated in Wilmington, Delaware, which is looking into the tax affairs of the president’s son, made the subject harder to avoid.

First there was Lunden Roberts, with whom Biden has a three-year-old unacknowledged child. Then Zoe Kestan, an ex-girlfriend and lingerie and textile designer, spent five hours giving testimony on Biden’s spending, including – reportedly – stays at the Chateau Marmont in Los Angeles, where, in 2018, allegedly, Biden was preoccupied with cooking crack cocaine.

Wretched and salacious as that sounds, much of Hunter Biden’s story, detailed at length in his autobiography Beautiful Things, published last year, tends that way. “I’m not a curio or a sideshow to a moment in history,” Biden claimed in his book. “I’ve worked for someone other than my father, [I] rose and fell on my own.”

But that’s not how Joe Biden’s political enemies see it.

Donald Trump tried to make issue out of Hunter’s business dealings in Ukraine, Russia and China, which included high paid consultancies and gifts, and allegations that, as vice-president, Joe Biden had shaped American foreign policy in Ukraine to benefit his son.

For Trump, it backfired, when efforts to uncover information about the Bidens and Ukraine helped to trigger his first impeachment. Then came the surfacing of Hunter Biden’s missing laptop, with its library of decadent pictures and business email chains, mysteriously left at a Wilmington repair shop, which found its way to Republican political operatives including Rudy Giuliani and Steve Bannon, plus the rightwing press and the FBI.

On the political flip-side, House intelligence committee chair Adam Schiff said the laptop was a “smear” from Russian intelligence, and 50 former intelligence officials said it was probably Russian disinformation. Now, however, almost no one disputes its authenticity.

Hunter Biden confirmed that he was under federal investigation over a tax matter in December 2020, days after his father was elected president. Attorney general Bill Barr said he had “not seen a reason” to appoint a special counsel to oversee investigations, which include an investigation by a federal securities fraud unit in New York and another in Pennsylvania.

Biden has not been charged with any crime, and David Weiss, US Attorney for Delaware who oversees the inquiry, is regarded as a straight-shooter unlikely to be swayed by political pressure. He was appointed by Trump on the recommendation of the state’s two Democratic senators and has not been replaced by Joe Biden.

Weiss, according to Politico, avoided taking any decisions that would alert the public to the existence of the inquiry before the 2020 presidential election – and a repeat of the FBI’s Hillary Clinton missing emails investigation, which may have influenced the outcome of the 2016 contest.

But the larger question – beyond whether Hunter Biden correctly met tax obligations during a period in which, by his own telling, he was being paid $50,000 a month by Ukrainian firm Burisma – are Biden’s financial ties to foreign figures and businesses while his father served as Barack Obama’s No 2.

Illegal lobbying is an issue that shadowed Trump throughout his presidency, leading to the conviction of Paul Manafort, Trump’s 2016 campaign manager, on tax fraud charges. Manafort later pleaded guilty to violating the Foreign Agents Registration Act (Fara) by providing false statements, laundering money, witness tampering and failing to register as an agent of the Ukrainian government.

Last year, Thomas Barrack, a friend and former adviser to Trump, was arrested on charges that he and others failed to inform the US government that they were working to influence US foreign policy on behalf of the United Arab Emirates.

Under US statutes, all persons acting politically or quasi-politically on behalf of foreign entities in the US must properly disclose their activities.

In addition to Hunter Biden’s ties to Ukraine through the gas company Burisma, he has sat on the boards of BHR Partners, a private investment fund backed by a number of Chinese state entities; a hedge fund, Paradigm; a consultancy, Seneca Global Advisors; and the fundraising firm Rosemont Seneca.

Republicans, including the senior Iowa senator Chuck Grassley, have called on the justice department to evaluate whether Hunter or Joe Biden’s brother James Biden should have registered as foreign agents over their business arrangements with the Chinese government-backed energy company CEFC.

In 2018, Business Insider reported that Hunter Biden sought an annual $2m retainer to aid in the recovery of Libyan assets frozen by the Obama administration during Muammar Gaddafi’s rule. The list of accusations goes on.

According to Jonathan Turley, a legal scholar at the George Washington University Law School, “influence-peddling is a virtual spectator sport in the nation’s capital – a protected corruption”.

Turley said: “It’s how powerful ruling elites make much of their money, and Congress has never seriously tried to crack down on it. The children and spouses of powerful leaders continue to receive windfall payments from companies and foreign interests, but we’ve never quite seen the likes of Hunter Biden’s enterprises. His contracts go beyond anything we’ve seen before.”

Joe Biden has long insisted that his son did nothing wrong. “There’s nobody that’s indicated there’s a single solitary thing that he did that was inappropriate, wrong … or anything other than the appearance,” Biden said two years ago.

But should the Delaware panel recommend criminal charges, it could ricochet around the second half of his father’s administration.

Like Barr, the current US attorney general, Merrick Garland, has declined to appoint a special counsel. But if Republicans gain control of the legislature in November, pressure to appoint a prosecutor will certainly build, as it did from Trump with Robert Mueller’s investigation into Russian election meddling or with Ken Starr, appointed to investigate the Clinton’s Whitewater investment dealings.

“I don’t have any doubts that if they [Republicans] can, they will,” said James Carville, architect of Bill Clinton’s 1992 presidential victory and Democratic party strategist throughout the 90s, with a long memory of politically inspired investigations.

“At first you’re outraged, then it becomes the standard routine of everyday life. You become battle-hardened and immune to it. I think they spent 687 hours investigating the Clinton Christmas card list – a major, major investigation. I can’t tell you the amount of coverage and investigations that went into Whitewater, which was nothing. [And] Travelgate. Then you end up with an act of consensual sex and they go, ‘A-ha! We were right the whole time!’”

But for presidential children, the stakes are different, and may have only have risen as Washington has become more partisan. “They find themselves in the spotlight whether they want to or not,” said Nancy Reagan biographer Bob Colacello.

“Lynda Bird Johnson dating playboy movie star George Hamilton, Ron Reagan dropping out of Yale to become a ballet dancer, his sister Patti Davis marching with Nuclear Freeze protesters, Chelsea Clinton flopping as a TV news reporter, the Bush girls partying at downtown Manhattan clubs … all were tempests in teapots compared to the mess Hunter Biden has got himself into with his questionable business ventures in China and Ukraine.”

One issue, says Kathleen Clark, a professor of Law at Washington University in St Louis, is that the financial conflict of interest law does not reach the adult children of elected officials. “There were similar, if not exactly parallel, problems with the adult children of Donald Trump trying to sell condos in India, [trying to] pursue business in other countries,” Clark points out.

But efforts to investigate the Trump family are faltering.

Last week, the New York district attorney’s investigation into whether the Trump Organization – which includes Trump sons Eric and Donald Jr as senior executives – inflated the value of assets to obtain favorable bank loans, appeared near to collapse when two prosecutors hired for the purpose resigned.

But the Delaware grand jury in Hunter Biden’s affairs has greater scope.

According to Tessa Capeloto, an attorney specializing in the Foreign Agents Registration Act at Wiley Rein, the impetus to look at influence-peddling violations has increased since a 2016 inspector-general’s report found that Fara was not being enforced as aggressively as needed.

“There’s been a concerted effort by DOJ to see that the statute has some teeth and is being effectively administered and enforced. The statute is out there for a reason, which is to ensure that certain political and quasi-political activities undertaken on behalf of foreign interests are reported and made transparent.”