This week will feature a record-breaker: the most expensive game of amateur golf in British, and probably world, history. A £5m price tag is being put on the Scottish leg of Donald Trump’s visit to these shores.

The Edinburgh government has been told that the Westminster government will pick up the bill for the security around his trip north of the border. Among Theresa May’s advisers, £5m is thought to be a price well worth paying. Hitting small white balls into holes keeps her volatile visitor distracted and off Twitter. As importantly, the trip north of the Cheviots will reduce the amount of time that he is in London, where protests against his presence in Britain are likely to be the largest.

Previous visits by American presidents have emphasised the historic bonds between the two countries and underlined a continuing closeness of values and interests. This much-delayed visit will stress the many strains in the relationship. There will be no carriage ride down the mall with the Queen or banquet at Buckingham Palace. He will be helicoptered between country residences and well-guarded stately homes. Rather than put the visitor near the British public, huge effort has gone into keeping him as far away from them as possible.

The security aspects of the visit have been giving nightmares to those in charge of it, but they are not the most anxiety-inducing dimension for Mrs May. Her largest concern is the political handling of her guest. This is a subject of such worry at the top of government that the cabinet recently even took a bit of time out from wrangling over Brexit to debate what to do. They did not come to any particularly useful conclusions other than that Mrs May will have to muddle through and pray that it is not a disaster.

The prime minister wants to minimise her public exposure to an American leader so unpopular with her own voters. At the same time she does not want to provoke her thin-skinned and mercurial guest.

The biggest risk to Mrs May is that she gets crushed in a hideous diplomatic crunch. The president’s visit to Britain will be preceded by a Nato summit in Brussels. The western alliance is brittle; relations between the US and its traditional allies in Europe have not been in such bad shape since the foundation of the mutual defence pact. If the summit explodes into rancorous quarrelling about the funding and future of Nato, Mrs May will be left stranded in the middle of the wreckage.

After his visit to Britain, Donald Trump flies to Helsinki to meet Vladimir Putin. It is not beyond the bounds of possibility – it is wise not to rule out anything with this president – that he could strike some kind of bargain with the autocrat of the Kremlin that undermines Europe’s security. How do you say cheers in Russian? A Trump-Putin love-in would make Mrs May look awful when two British citizens have just become the victims of the novichok bio-weapon.

Even the most skilful of people handlers would have a hard time managing this American president. And Mrs May is not a brilliant people handler. Her personal chemistry with him is poor. She looked like a supplicant desperate for his goodwill when she made her dash to the White House early in his presidency and got nothing to show for it beyond some toe-curling pictures of the two of them awkwardly holding hands. The only relief for British officials was that he did not grab a different part of the prime minister’s anatomy. At last month’s G7 summit in Quebec, he omitted Mrs May from a list of other leaders whom he claimed to have good relations with. Whether this was a deliberate slight or just negligence, who can say? He is capable of both.

It is one of the many alarming things about Trump that he rarely meets an autocrat that he does not take to

There is one consolation for fretful British officials: none of the other traditional allies of America have found a way to conduct a fruitful relationship with this president. Justin Trudeau of Canada was the target of Trumpian vilification as a “backstabber” when that G7 collapsed into acrimony. Angela Merkel’s coolly diplomatic suggestions that America should remain true to democratic values have earned her the naked contempt of the occupant of the Oval Office. There was a period when Emmanuel Macron appeared to be establishing a strange kind of bromance after he invited the American president to join last year’s Bastille Day parade. His guest loved the display of flags and military hardware so much that he went home demanding one of his own. British officials, always neurotic about their country’s status in Washington, became twitchy when the French president boasted of “a very special relationship” with America. The British over-worried. True, Mr Macron got a return trip to Washington and an opportunity to address the joint houses of Congress. Yet, when it comes to substance, it is hard to see what the French president has actually achieved. His pleas for policy shifts by Washington have been unrequited. He tried to persuade the American to rework the nuclear deal with Iran; Mr Trump just tore it up regardless, as he also shredded America’s commitment to the Paris agreement on climate change.

No one has worked harder to woo him than Shinzo Abe, the prime minister of Japan and the first world leader to pay court at Trump Tower. His many efforts to flatter this president have not won him sufficient respect to get advance warning of Trumpian gambits towards North Korea, despite Japan’s keen concern about what happens with the nuclear weapons state just over the sea. Much of Japan’s prosperity hangs on the prowess of its export industries. The escalating trade war triggered from the Oval Office is very much not in its interests. Mrs May ought to note that fawning to Donald Trump does not work. He reads it as weakness.

His behavioural patterns suggest that one way to establish a relationship with this president is not to be one of the US’s traditional friends, but to be one of America’s historic adversaries. Vladimir Putin has often been lavished with Trumpian expressions of admiration. It is one of the many alarming things about him that he rarely meets an autocrat that he does not take to. This includes Kim Jong-un, “a very talented man” with whom he’d forged a “very special bond”, gushed the American after his summit with North Korea’s brutal dictator. Perhaps Mrs May’s best bet – I make this suggestion only half in jest – would be to remind the American president that the British burnt down the White House in 1814. Maybe that would get his respect.

Britain’s primary objective is to prevent the disintegration of Nato, the cornerstone of our security since the 1940s. Some counsel Mrs May that she should play to the Trump ego by reminding him that he is the leader of the world’s largest military alliance and then invite him to consider whether it would not be self-defeating to wreck the transatlantic defence pact. This makes the reckless assumption that alliances matter to him when evidence suggests the reverse.

Others tell her to remember that he is “transactional”. If you need something, you have to offer something. He wants Europeans to pay more towards Nato. This is not a new American demand. Previous presidents have complained that Europe is not pulling its military weight. It is not actually an unreasonable demand. He has a point when he says that the continent has for too long taken it for granted that the US will carry on protecting Europe while Europeans ran down their defence spending. I am sure Mrs May would love to be able to save the western alliance by making him an offer about Nato funding, but that is not in her capacity to give. Whatever political capital she possesses will be spent trying to sell the latest Brexit “peace deal”, which she brokered through the cabinet at Chequers on Friday. She doesn’t have the muscle to cajole European countries to stump up more for their defence.

It may be that all the energy expended by Number 10 trying to come up with ways to “manage” this American president is simply wasted. Making it a goal to have a good relationship with Donald Trump is fruitless because this is a man not interested in reciprocating. Trying to “manage” him makes as much sense as talking about managing a tornado. The only viable strategy available to Mrs May is to shutter the windows, tie down anything loose, weather the storm and control the damage as best she can.

• Andrew Rawnsley is an Observer columnist