Our Queen is used to dealing with the good, bad and ugly of US politics – but can she tame Trump?

"It's supposed to be a joke!" I screamed down the phone at the tabloid reporter who was trying to turn a tongue in cheek remark about Donald Trump into a sensational splash. The line was taken from an imagined scene in my book on the royal finances where the Queen is warned by a tax adviser of the risk of her estate being partly sold off to pay death duties:

"Would Her Majesty really want a situation where Prince Andrew is forced to sell his share of Balmoral to some overseas property developer – say, Donald Trump – who might turn the golf course and grounds into a luxury leisure centre for American multi-millionaires?"

Little did I imagine that two years later the joke would be on me when the said tycoon would be invited by the Queen to visit Britain and that one of his first reported requests would be to play a round of golf at Balmoral while Her Majesty looked on.

On Friday Theresa May announced at the White House that President Trump had accepted an invitation from Her Majesty to pay a state visit later this year. The exact itinerary of events has yet to be spelt out but it's likely to include a state banquet and an overnight at either Buckingham Palace or Windsor Castle. Any trip to Balmoral might depend on whether the state visit coincides with the Queen's traditional stay there in August and September.

Initially the news was greeted with a sense of guarded anticipation. If nothing else, the visit would showcase the longstanding ties been the two nations – or what Theresa May called in her joint press conference "the bonds of history, of family, kinship and common interests."

But Trump's controversial travel ban on citizens from seven, mainly Muslim countries has now put the whole trip in jeopardy. Bolstered by a petition with more than one million signatures, political leaders from Jeremy Corbyn and Tim Farron to Sadiq Khan and Alex Salmond have all called for the invitation to be withdrawn – at least until the ban is lifted.

Even if the trip does go ahead – as Downing Street now says it will – others fear that the unpredictable Trump may not behave. If he can grab the hand of the prime minister at the White House, what could he do when he has to bow to the Queen? Will he be able to resist the urge to trumpet her private remarks on his Twitter feed?

And what happens if the topic of climate change comes up when Prince Charles is present? Downing Street, according to a White House source, has already had high level discussions about avoiding such a clash and there is now talk of Charles avoiding the state banquet just as he did when Chinese President Xi Jinping dined at the palace in 2015.

So, what else might the Queen do to placate the president?

In a lifetime of playing host to world leaders (including ten American presidents) the Queen will have got used to dealing with the good, the bad and the ugly. When in June 1982 Ronald and Nancy Reagan became the first US presidential couple to have a sleepover at Windsor Castle, she agreed to the White House's request to go riding in Great Park and the sight of the two heads of state on horseback became one of the most emblematic images of his presidency.

Back in October 1970 the Queen was caught in the fly-on-the-wall documentary "The Royal Family" having to make stilted small-talk to Richard Nixon after a sudden stopover by the US president forced her to fly down from Balmoral to greet him at Chequers.

And then in April 2009 when the yelling of the Italian prime minister Silvio Berlusconi interrupted a G20 summit photo call at Buckingham Palace, she silenced him by dramatically flinging her arms in the air and asking "What is it? Why does he have to shout? Why!" The video went viral.

So, what can Her Majesty's Government actually gain from Trump taking tea with the Queen? To the Conservative MP Jacob Rees-Mogg, it's an opportunity for Britain to deploy its "secret weapon in foreign affairs" since "heads of state even of the most powerful countries such as China and the United States want to meet and get to know the Queen."

A less diplomatic way of describing this sort of access was the instruction given to Sir Christopher Meyer when he was made Washington ambassador after the election of President George W Bush: "we want you to get up the arse of the White House and stay there."

The Foreign Office must hope that the state visit would encourage the "America First" president to avoid turning his back on the world by endorsing the NATO alliance, forging closer links with Britain and in particular moving swiftly towards a bilateral trade deal.

Trump won't be the first – nor the last - American billionaire to cosy up to the royal family.

So, what can a super-patriot president actually gain from kow-towing to another head of state? As someone whose image was sculpted by television, Trump knows the power of good optics. By sharing a gilded royal carriage with the most famous woman in the world, he will hope that some of the fairy dust will fall on his golden coif.

Trump won't be the first – nor the last – American billionaire to cosy up to the royal family. The Texan banker Joe Allbritton curried favour with the Prince of Wales by donating a small fortune to Charles's charities and lending him his private Gulfstream jet. At least since the days of Edward VII – whose court was chock-a-block with shady businessmen like Cecil Rhodes and Horace Farquhar –the monarchy has attracted new money as those in search of status trade cash for an easy entrée into smart society.

Trump may have used his wealth to buy the Turnberry golf resort but there remains many clubs who would not want him a member. If and when he is invited by the Queen to tee-off at Balmoral, there's only likely to one winner in a contest between the crass and class.

David McClure is the author of Royal Legacy (Thistle Books 2015)