Tallying up the daunting inventory of demands on the new prime minister's time, it's a wonder Theresa May wants the job at all.

There's Brexit -- which she didn't support but equally didn't not support -- and the fallout from that. When does she trigger Article 50? Will an "independent" Britain be in the European Economic Area? Does that mean we'll have to accept some measure of freedom of movement? Can Angela Merkel be won round to a jolly old British compromise between these conflicting positions?

And that's not to mention reshuffling her Cabinet, steering the economy back on course, and setting out a domestic agenda of her own.

At this point, Scotland seems like a trifling concern but the Prime Minister Unelect ignores it at her peril. Brexit has played out differently north of the border, where the anguish of Remainers is shared across the political spectrum and crucially by the Scottish Government. Scotland voted to stay and people are not happy that their future is tied to a split from the EU that 62% of us didn't want.

First Minister Nicola Sturgeon wants to keep Scotland within the community and has been holding meetings with European leaders, bureaucrats and rat-catchers to that end. If she isn't successful, the Nationalist leader warns, a second referendum on independence is back on the table. Sturgeon was beaming all through the men's singles final at Wimbledon yesterday, and not just because Scot/Brit (fight it out amongst yourselves) Andy Murray smashed it once again. The polls show that if independence comes to match point again, it's very much advantage SNP.

So how does the new PM handle the restless natives in the north?

The SNP is expert at mining grievance from even the most innocuous act or statement. Theresa May could wallpaper Number 10 in tartan and change the national anthem to Ye Cannae Fling Pieces Oot A 20-Storey Flat and still the Nationalists would claim Scotland was being simultaneously ignored and victimised by Westminster. The Cameron administration too often found itself on the back foot because it tried to act in good faith, grasping too late that it was dealing with a never-ending political campaign rather than a government.

Outwardly, May must be seen to accord the Scottish Government due respect. Her first visit after kissing hands with the Queen should be an audience with the Queen of Scotland. Prime Minister May should do the photo-op on the steps of Bute House and tell the cameras she has come to consult and work with her colleague Nicola. Scotland voted Remain by a clear margin and the UK-wide result has understandably caused anger and concern north of the border. As a Remain supporter, she should say, I voted the same way as 1.6 million Scots and I appreciate that they want to maintain a strong relationship with Europe. I will be working with the First Minister and European leaders to get the best deal for Scotland while carrying out the democratic will of people across the UK.

What that relationship would look like and whether it is even achievable is up to May and, ultimately, France and Germany. But May has to stand up visibly for the Scottish majority and reassure them she's on their side and will fight their corner in Brussels too, not just that of Brexiteers and her right-wing backbenchers. This is how she gets a hearing in Scotland, and the time to pursue negotiations for her version of Brexit. If she mishandles the Scottish dimension, a second independence referendum is all but inevitable and a second No vote far from guaranteed.

Once inside Bute House, May should get tough. Yes, she respects the Scottish Government's position. Yes, she will make Scotland's relationship with the EU a key point in her negotiating agenda with Brussels. She might even be open to the Edinburgh ministry recommending 50% of Team Scotland negotiators. But the constitutional game-playing, the indyref2 threats -- these all stop. Sturgeon can be an equal partner in a grown-up political process or she can pander to her excitable grassroots; she can't do both.

Britain's second female leader should tell Scotland's first that she does not consider Brexit a "material change in circumstances" that would justify a second independence referendum. Scotland voted No, barely two years ago, and by a margin of almost 11 points. That majority of Scots deserves to have its will respected as much as the majority who voted for Remain. May should avoid ruling out an independence rerun, a belligerent stance that would only boost backing for a breakaway, but insist that any do-over would be in the gift of the UK Parliament (with full consultation of Holyrood). It is not an outcome to be realised by piggybacking on a British constitutional crisis.

Ultra-unionists, such as remain in Scotland, might want a firmer stance, preferring May to reject a second Scottish plebiscite out of hand. That would be a lamentable error, shifting the campaign for independence from the Scottish Parliament out into the streets, the Nationalists rallying tens of thousands of protesters on the justifiable grounds that Scotland was being held hostage by a Tory government. A Caledonian Catalonia would be a far worse outcome than even a messy divorce.

By keeping the possibility of independence alive, May acquires more firepower against her right flank. Push me too far on Brexit conditions and we could lose Scotland, would be her underlying message (underlying that: And maybe Northern Ireland too).

Despite some new recruits, and the old generals rolling out their rusty artillery, federalism is a spent force in British politics. In many regards, the Scottish Parliament has powers far in excess of any federal legislature around the world and the constitutional particulars of four nations, plus London, plus the English regions are too divergent to contain in even a flexible federal structure. It's the Union or bust from here on in.

Instead of running away from devolution, as some nominal Unionists now are, May ought to see Brexit as an opportunity to reassert the case for the Union. An organic and malleable Union, one still capable of reform, but an arrangement endorsed by the Scottish people in 2014 and one which serves the country well. If you seek a monument to storming out of a successful political and economic compact, look around you.

May has to grasp what David Cameron only latterly did, what the Nationalists strive to play down, and what Ruth Davidson has banged on about for years: Scotland has two governments. The UK Tories allowed Scotland to become an afterthought -- "that's Labour's responsibility" -- and paid for that complacency with a near-miss in September 2014. Next time, it might not be a miss. Scotland in turn has come to think of Westminster as "that other place", less significant in our lives than Holyrood, and because of distance and ignorance and lack of engagement, what significance we do accord it is malign.

Scottish newspapers and news programmes publish and broadcast less UK political content than a decade ago. Westminster makes the news when it's dragging us out of the EU, debating whether to bomb another Middle Eastern country, embroiled in scandal, or riven by division over the Labour leadership. This is not a function of bias or laziness on the part of Scottish news organisations. It's all about the numbers. Journalists are bombarded with Scottish Government press releases all day long; we are lucky to get one or two a day from the UK Government and those are almost always from the Scotland Office.

Comms might seem a bit below the PM's pay grade but the poli tics of the Union is a war of perception and at present the UK Government is barely visible on the battlefield. And it's not just a PR problem; it is about taking a holistic approach to government (don't worry, my toes curled writing it too). Scotland is not the preserve of Dover House and, from time to time, the Treasury; it should be a key concern across government, even in areas where many if not all responsibilities are devolved to Edinburgh. There should be a desk in every department tasked with crafting Scotland-related policy, bringing a Scottish perspective to bear on decision-making and policy implementation, and flagging up potential snafus between devolved and reserved responsibilities. The UK Government does not stop at the Tweed and pick up again at Faslane and Coulport.

Theresa May must be respectful and measured but she must also challenge the perception that the Prime Minister is a foreign dignitary when visiting Scotland. The Union remains on precarious ground and, in delivering Brexit and beyond, the woman now charged with holding it together should reject David Cameron's benign neglect.

Two women now call the shots in Scotland and Nicola Sturgeon is just one of them.

Comment by Stephen Daisley, STV's digital politics and comment editor. You can contact him at stephen.daisley@stv.tv.