Something tells me this is not the beginning to the fifth session of the Scottish Parliament Nicola Sturgeon had in mind.

First was the election result, both triumph (more than a million votes) and modest disaster (the loss of an overall majority), and it quickly became clear this wasn’t on the grid; the SNP tried to carry on as if nothing had changed, but it had.

Then last Tuesday Ms Sturgeon’s re-election as First Minister was overshadowed by a story in a tabloid newspaper concerning two of her party’s Westminster MPs, one of whom, Stewart Hosie, was also her deputy.

The impact of that was less about the sexual impropriety and more about the relationships involved: Ms Sturgeon, Mr Hosie and the latter’s wife, Health Secretary Shona Robison, have known each other since the late 1980s. In such a tight-knit party like the SNP, that was never going to be easy.

Having made a point of hugging Ms Robison in the Chamber shortly after her re-election, the First Minister tried to duck questions from the media as to whether Mr Hosie retained her confidence. Asked during an impromptu press briefing in a lift, Ms Sturgeon repeatedly said the story was a “private matter” and Mr Hosie was “elected as deputy leader of the party”.

That bland statement of the obvious indicated all was not well. The SNP MSPs I spoke to that afternoon expressed doubt Mr Hosie would end up leading the summer independence “initiative” but didn’t think he would lose anything beyond that. There was, however, a notable absence of warmth, for the outgoing deputy leader of the SNP doesn’t seem to have generated much affection, even within his own ranks.

His leader, meanwhile, has acted decisively and, it has to be said, quite ruthlessly (though with justification). Had Alex Salmond still been leader Mr Hosie might have been able to tough things out, but he had become a problem to be managed and yesterday afternoon we saw the damage-limitation exercise kick in, a confirmation he would not seek re-election as “Depute Leader” (the SNP’s preferred formulation) at this year’s autumn conference, while Pete Wishart MP asked the Metropolitan Police to investigate the Conservative Party’s 2015 campaign expenditure in a desperate attempt to limit the coverage in today’s newspapers.

In his letter to Ms Sturgeon, Mr Hosie cited his constituency, his family and his health, but the first sentence, apologising for the “hurt and upset” caused to “friends, family and colleagues”, betrayed the reality. The First Minister’s reply – which didn’t mention Mr Hosie’s health – was brisk, thanking him for his year and a half of service and his work on the 2015 and 2016 SNP manifestos. “I have enjoyed working with you as Depute Leader,” it concluded unconvincingly, “and I look forward to continuing to work with you in the future.”

So what does it all mean? On one level, not very much. Being deputy leader of the SNP has never been a particularly significant position (the same is true of other parties’ deputies, just look at Harriet Harman), and the same has been true of the past nine years in devolved government. It brings to mind John Nance Garner’s memorably crude remark about the Vice-Presidency of the United States not being “worth a bucket of warm piss”.

Thus later this year candidates will emerge to succeed Mr Hosie, most likely safe pairs of hands who represent no threat to the First Minister. John Swinney might choose to formalise his status as Ms Sturgeon’s de facto deputy, while Cabinet Secretary Keith Brown – the surprise loser in late 2014 – might have another go. Humza Yousaf, who missed out on a Cabinet position last week, is another possibility, as is Angus Roberston MP, while it might be an idea for the party to find someone who can handle economics with more aplomb than its leader.

But there is scope for something more interesting to happen. There’s a perception in some sections of the SNP that the Nicola Sturgeon/Peter Murrell duopoly is too dominant. That’s one reason the former First Minister Alex Salmond stood for and won election to the party’s National Executive Committee (though that long ago ceased to have a significant governance role) last year, so perhaps on a similar basis someone might (diplomatically) pitch themselves as a counterbalance to that.

There remains a strategic divide in the SNP between those who believe each passing week diminishes its ability to seize the moment when it comes to another independence referendum and those (like the First Minister) who want to bide their time. Could someone stand for the deputy leadership with a commitment to including indyref2 in the next manifesto? It’s not impossible, and as I say there is an appetite within the party to check the dominance of party HQ.

Beyond that possibility – and one assumes the leader will make sure it doesn’t happen – the political fallout from last week’s tabloid stories will further fuel media and opposition narratives about “peak SNP”, or even “peak Nicola”. Third terms for governing parties – even hugely popular ones like New Labour – are notoriously problematic, for the usual vagaries of the political cycle tend to kick in.

And while Mr Hosie and Angus MacNeil, who also had an affair with journalist Serena Cowdy, are both long-serving MPs, they form part of a group of SNP MPs that were supposed to be doing things differently, standing up for Scotland at Westminster rather than indulging themselves like so many others over the decades. Thus the party’s time-honoured tendency to occupy the moral high ground has resulted in the usual tales, financial and sexual, that generate the impression the “new politics” is just like the old, only with lashings of added sanctimony.

Yesterday Ian Murray, Labour’s Shadow Scottish Secretary, drew exactly that point. “Last year the SNP told us their MPs would be stronger for Scotland, but just 12 months on many have been a source of real embarrassment.” He meant, of course, not only Mr Hosie and Mr MacNeil, but also Natalie McGarry, Michelle Thomson, Phil Boswell et al. And while having dozens more parliamentarians is obviously a good thing for any party, it also means more stuff can go wrong.

The First Minister and her colleagues are clearly unhappy – indeed senior SNP “sources” were unusually vocal, nay brutal, in their briefings to Sunday newspaper journalists – and understandably so, for the party rightly views its cast-iron discipline as one of its main electoral assets over the past decade. Ms Sturgeon might be a strong leader but she can’t control everything that happens in her party, and naturally it will eventually (if not yet) reflect badly on her.

Even so, talk of “peak SNP” is premature. The SNP remains popular and so does its leader, but perhaps in a few years’ time commentators might look back on the early days of the fifth parliamentary session as the moment at which events, dear boy, events, gradually began to reverse the party’s extraordinary period of Teflon-coated dominance.